Exhibit 10.1

Execution Version

FIRST AMENDMENT TO THE AMENDED AND RESTATED PLAN SUPPORT AGREEMENT

This First Amendment to Amended and Restated Plan Support Agreement (this “First Amendment”) is entered into as of July 31, 2012, by and among (i) Dynegy Inc. (“Dynegy”), (ii) Dynegy Holdings, LLC (“DH”), (iii) the Consenting Senior Noteholders (as defined below), (iv) the Consenting Lease Certificate Holders (as defined below), and (v) Resources Capital Management Corporation (“RCM” and collectively, the “Amendment Parties”).

W I T N E S S E T H

WHEREAS, reference is made to that certain Amended and Restated Plan Support Agreement, dated as of May 30, 2012 (the “Plan Support Agreement”), by and among (i) Dynegy, (ii) Dynegy Gas Investments, LLC, (iii) Dynegy Coal Holdco, LLC, (iv) DH, (v) Dynegy Danskammer, L.L.C. (“Dynegy Danskammer”), (vi) Dynegy Roseton, L.L.C. (“Dynegy Roseton”), (vii) Dynegy Northeast Generation, Inc. (“DNE”), (viii) Hudson Power, L.L.C. (“Hudson”; each of DH, Dynegy Danskammer, Dynegy Roseton, DNE and Hudson are debtors and debtors in possession in the jointly administered chapter 11 cases styled as In re Dynegy Holdings, LLC, et al., Case No. 11-38111 (CGM) (the “DH Cases”), and are collectively referred to herein as the “DH Debtors”), (ix) the beneficial owners (or advisors, nominees or investment managers for the beneficial owner(s)) of a portion of the outstanding Senior Notes (as defined in the Plan Support Agreement) issued by DH who are parties thereto, solely in their capacities as holders of such Senior Notes and not in any other capacity (the “Consenting Senior Noteholders”), (x) RCM, Resources Capital Asset Recovery, L.L.C., Series DD and Series DR, Roseton OL LLC, Danskammer OL LLC, Roseton OP LLC, and Danskammer OP LLC, (xi) the beneficial owners (or advisors, nominees or investment managers for the beneficial owners(s)) of a portion of the Lease Certificates (as defined in the Plan Support Agreement) who are parties thereto, solely in their capacities as holders of such Lease Certificates and not in any other capacity (the “Consenting Lease Certificate Holders”), (xii) DO S1 Limited, (xiii) Loomis, Sayles & Company, L.P., solely in its capacity as a holder of NGC Trust Capital Income Securities, and (xiv) Claren Road Asset Credit Master Fund Ltd.;

WHEREAS, on June 18, 2012, DH filed with the United States Bankruptcy Court for the Southern District of New York, Poughkeepsie Division (the “Bankruptcy Court”) that certain Modified Third Amended Chapter 11 Plan of Reorganization for Dynegy Holdings, LLC proposed by DH and Dynegy [DH Case Docket No. 805] (the “Plan”), and related disclosure statement [DH Case Docket No. 804] (the “Disclosure Statement”);

WHEREAS, on June 18, 2012, DH also filed with the Bankruptcy Court a Supplemental Motion for an Order (I) Approving the Disclosure Statement; (II) Approving Solicitation and Voting Procedures; (III) Scheduling the Plan Confirmation Process; and (IV) Granting Related Relief [DH Case Docket No. 801],  along with forms of notice and ballots attached as exhibits thereto, which motion supplemented and amended the relief sought by the Motion of Dynegy Holdings, LLC for an Order (I) Approving the Disclosure Statement; (II) Approving Solicitation and Voting Procedures; (III) Scheduling the Plan Confirmation Process; and (IV) Granting Related Relief [DH Case Docket No. 124], filed by DH on December 1, 2011;

WHEREAS, on July 3, 2012, in the DH Cases, the Bankruptcy Court entered an Order (I) Approving (A) the Disclosure Statement; (B) Solicitation and Voting Procedures; and (II) Scheduling the Plan Confirmation Process [DH Case Docket No. 847] (the “DH Disclosure Statement Order”), which authorized DH and Dynegy, in the event Dynegy later commenced a chapter 11 case in the Bankruptcy Court, among other things, to modify the Plan and Disclosure Statement as necessary to constitute a plan of reorganization and disclosure statement for both DH and Dynegy, both as debtors;

WHEREAS, on July 6, 2012, Dynegy filed a voluntary petition for relief under chapter 11 of the Bankruptcy Code with the Bankruptcy Court, and became a debtor in the separately administered chapter 11 Case No. 12-36728 (CGM) (the “DI Case”);

WHEREAS, on July 6, 2012, Dynegy filed the Motion for Entry of an Order (I) Directing Joint Administration of the Dynegy Inc. Chapter 11 Case with the Chapter 11 Cases of Its Affiliated Debtors, (II) Directing that Certain Orders Entered in the Chapter 11 Cases of the Affiliated Debtors be Made Applicable to the Dynegy Inc. Chapter 11 Case, (III) Authorizing the Solicitation of Votes With Respect to Dynegy Inc. in Accordance With the Terms of the Disclosure Statement Order, and (IV) Postponing the Meeting of Creditors Under 11 U.S.C. § 341(A) [DI Case Docket No. 2], which requested, among other things, that the Bankruptcy Court enter an order directing that certain orders previously entered in the DH Cases, including the DH Disclosure Statement Order, be made applicable to the DI Case;

WHEREAS, on July 10, 2012, the Bankruptcy Court entered that certain order (I) Approving (A) the Disclosure Statement; and (B) Solicitation Procedures; and (II) Scheduling the Plan Confirmation Process [DI Case Docket No. 21] (the “DI Disclosure Statement Order” and together with the DH Disclosure Statement Order, the “Disclosure Statement Orders”), which, among other things, approved the Disclosure Statement in the DI Case and also authorized DH and Dynegy to modify the Plan and Disclosure Statement as necessary to constitute a plan of reorganization and disclosure statement for both DH and Dynegy, both as debtors;

WHEREAS, in accordance with the Disclosure Statement Orders, Dynegy and DH (together, the “Plan Debtors”) have made certain modifications to the Plan (as so modified, the “Joint Plan”) and the Disclosure Statement (as so modified, the “Joint Disclosure Statement”), to reflect the commencement of the DI Case and so that they constitute a plan of reorganization and disclosure statement for both Plan Debtors;

WHEREAS, on July 12, 2012, the Joint Plan and Joint Disclosure Statement [DI Case Docket No. 28; DH Case Docket No. 861] were filed with the Bankruptcy Court;

WHEREAS, in connection with the Joint Plan and Joint Disclosure Statement, the Amendment Parties now wish to make certain related modifications and conforming changes to the Plan Support Agreement;

WHEREAS, Section 23 of the Plan Support Agreement provides that the Plan Support Agreement may be modified or amended by written agreement executed by Dynegy, DH, a

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Majority of the Consenting Senior Noteholders (as defined therein) and a Majority of the Consenting Lease Certificate Holders (as defined therein) and RCM, and as so amended shall be binding on all the Parties (as defined therein) to the Plan Support Agreement; and

WHEREAS, the Amendment Parties desire to amend the Plan Support Agreement in accordance with Section 23 thereof.

NOW, THEREFORE, in consideration of the covenants and agreements herein contained and other good and valuable consideration (the receipt and sufficiency of which are hereby acknowledged), the Parties hereby covenant and agree as follows:

1.                                       Capitalized terms used herein and not otherwise defined herein shall have the respective meanings ascribed to such terms in the Plan Support Agreement.

2.                                       Section 1 of the Plan Support Agreement shall be amended to add the following definitions:

(a)                                  “Conforming Plan Determination” means any determination by the Bankruptcy Court with respect to a Non-Conforming Plan Assertion other than a Non-Conforming Plan Determination.

(b)                                 “Effective Date Milestone” shall have the meaning ascribed to it in Section 12.(b)f. hereof.

(c)                                  “Non-Conforming Plan Assertion” means an assertion by either (a) the Majority Consenting Senior Noteholders or (b) the Majority Consenting Lease Certificate Holders that the Plan is not a Conforming Plan because of Claims asserted against Dynegy, pursuant to a formal written notice that states on its face that it is a “Non-Conforming Plan Assertion” and which is delivered to Dynegy and each other Party in accordance with the notice provisions of Section 21 of this Agreement.

(d)                                 “Non-Conforming Plan Determination” means a determination by the Bankruptcy Court that the Plan is not a Conforming Plan because of Claims asserted against Dynegy as specified in the Non-Conforming Plan Assertion.

(e)                                  “Plan Confirmation Milestone” shall have the meaning ascribed to it in Section 12.(b)e. hereof.

3.                                       Section 2 of the Plan Support Agreement shall be amended as follows:

(a)                                  by deleting the word “and” at the end of clause e thereto;

(b)                                 by replacing the period at the end of clause f thereto with “; and”; and

(c)                                  by adding the following new clause g immediately after clause f thereto:

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g.                                      in the case of Dynegy, agrees to (x) provide to the other Parties (and to the Creditors’ Committee) by August 6, 2012, copies of all proofs of claim timely filed against Dynegy (and to provide copies of any untimely proofs of claim promptly after receipt thereof), and (ii) provide on an expedited basis any reasonably requested diligence materials relating to any claims filed against Dynegy, in each case to the other Parties (and to the Creditors’ Committee).

4.                                       Sections 9(a)(3) and 14(iv) of the Plan Support Agreement shall in each case be amended to change “September 10, 2012” to “the Plan Confirmation Milestone”.

5.                                       Sections 9(a)(4) and 14(v) of the Plan Support Agreement shall in each case be amended to change “October 1, 2012” to the “Effective Date Milestone.”

6.                                       Section 12.(b)e. of the Plan Support Agreement shall be amended to change “September 10, 2012” to “September 21, 2012 (or, in the event of a Non-Conforming Plan Assertion, such later date as may be applicable pursuant to Section 34(c)) (the “Plan Confirmation Milestone”).”

7.                                       Section 12.(b)f. of the Plan Support Agreement shall be amended to add the following after “October 1, 2012” and before the semicolon: “(or, in the event of a Non-Conforming Plan Assertion, such later date as may be applicable pursuant to Section 34(c)) (the “Effective Date Milestone”).”

8.                                       Section 20 of the Plan Support Agreement shall be amended to delete the second sentence thereof and replace it with the following:  “For the avoidance of doubt, (a) the Lease Trustee is an intended third-party beneficiary of Sections 2.a, 5, 21 and 23 hereof, (b) subject to Section 27 of this Agreement, the Creditors’ Committee is an intended third-party beneficiary of Sections 2.a, 2.g, 5, 7, 8, 21, 23, 27, 30 and 34(e) hereof, and (c) the Subordinated Notes Indenture Trustee is an intended third-party beneficiary of Section 2.a.ix. hereof.”

9.                                       The first proviso of Section 23 of the Plan Support Agreement shall be amended to delete the reference to “Sections 2.a, 5, 7, 8, 21, 23, 27 and 30 hereof” and replace it with the following “Sections 2.a, 2.g, 5, 7, 8, 21, 23, 27, 30 and 34(e) hereof.”

10.                                 The following new Section 34 shall be added to the Plan Support Agreement:

34.                               Non-Conforming Plan Assertions.  A Non-Conforming Plan Assertion may be made only by the Majority Consenting Senior Noteholders or the Majority Consenting Lease Certificate Holders as set forth herein, and a Non-Conforming Plan Assertion may not be made by any other Party or intended third-party beneficiary under this Agreement.  The Parties each agree that in the event of a Non-Conforming Plan Assertion:

(a)                                  the applicable Parties shall (x) seek a Conforming Plan Determination or Non-Conforming Plan Determination on an expedited basis and (y) request that the Bankruptcy Court set a hearing date no later than twenty (20) days after the delivery of such Non-Conforming Plan Assertion;

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(b)                                 the Parties shall not seek, shall not direct any other person to seek, and shall not support any other person (including the Creditors’ Committee) in seeking, appellate review of any Conforming Plan Determination or Non-Conforming Plan Determination;

(c)                                  if, as of September 21, 2012, the Bankruptcy Court has not yet rendered a Conforming Plan Determination or a Non-Conforming Plan Determination, (x) the Plan Confirmation Milestone shall be extended to the date that is five (5) days after the Bankruptcy Court makes a Conforming Plan Determination or a Non-Conforming Plan Determination; and (y) the Effective Date Milestone shall be extended to the date that is fifteen (15) days after the Plan Confirmation Milestone;

(d)                                 if a Non-Conforming Plan Assertion is delivered by either the Majority Consenting Senior Noteholders or the Majority Consenting Lease Certificate Holders, but not both, the Parties who did not deliver a Non-Conforming Plan Assertion shall not be permitted to deliver a Non-Conforming Plan Assertion once the Bankruptcy Court renders a Conforming Plan Determination or a Non-Conforming Plan Determination; and

(e)                                  if, and only if, a Non-Conforming Plan Assertion is delivered by the Majority Consenting Senior Noteholders or the Majority Consenting Lease Certificate Holders, the Creditors’ Committee may appear and be heard in connection with the prosecution of such Non-Confirming Plan Assertion in the Bankruptcy Court, including with respect to any request made to the Bankruptcy Court by Dynegy, the Majority Consenting Senior Noteholders and/or the Majority Consenting Lease Certificate Holders to reconsider a Conforming Plan Determination or a Non-Conforming Plan Determination; provided, that (i) the Creditors’ Committee (x) shall not seek, shall not direct any other person to seek, and shall not support any other person in seeking, appellate review of any Conforming Plan Determination or Non-Conforming Plan Determination; and (y) shall not file, maintain or otherwise initiate any request for reconsideration of a Conforming Plan Determination or a Non-Conforming Plan Determination; and (ii) in the event that Dynegy and the Party or Parties who have made a Non-Conforming Plan Assertion agree to a consensual resolution of such Non-Conforming Plan Assertion in lieu of any litigation or further litigation thereof, the Creditors’ Committee shall have no further right to appear and be heard in connection with, and shall have no independent rights in respect of, any such Non-Conforming Plan Assertion, including with respect to the prosecution of such Non-Conforming Plan Assertion or reconsideration of a Conforming Plan Determination or a Non-Conforming Plan Determination.

11.                                 Other than as expressly amended by this First Amendment, the Plan Support Agreement remains in full force and effect in accordance with its original terms.

12.                                 This First Amendment shall be governed by and construed in accordance with the laws of the State of New York, without regard to the conflict of laws principles thereof.  Any

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action brought in connection with this First Amendment shall be brought in the Bankruptcy Court, and the Parties hereby irrevocably consent to the jurisdiction of such court and waive any objections as to venue or inconvenient forum.

13.                                 All modifications and amendments to this First Amendment or any part hereof shall be made in accordance with Section 23 of the Plan Support Agreement.

14.                                 This First Amendment may be executed in counterparts and signature pages exchanged by facsimile or by other electronic form, and each counterpart shall be deemed to be an original, but both counterparts of which shall constitute the same agreement.

15.                                 Each person who executes this First Amendment on behalf of a Party represents that he or she is duly authorized to execute this First Amendment on behalf of such party.

16.                                 This First Amendment is not and shall not be deemed to be a solicitation of votes for the acceptance of the Plan (or any other plan of reorganization) for the purposes of sections 1125 and 1126 of the Bankruptcy Code or otherwise.

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Execution Version

IN WITNESS WHEREOF, the Parties hereto have executed this First Amendment as of the date set forth above.

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Execution Version