Exhibit 4.1

OFFSHORE GROUP INVESTMENT LIMITED

AND EACH OF THE GUARANTORS PARTY HERETO

11 ¹/₂% SENIOR SECURED FIRST LIEN NOTES DUE 2015

SEVENTH SUPPLEMENTAL INDENTURE

Dated as of December 3, 2012

Wells Fargo Bank, National Association,

as Trustee and Noteholder Collateral Agent

THIS SEVENTH SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of December 3, 2012, is by and among Offshore Group Investment Limited, a Cayman Islands exempted company (the “Company”), Vantage Drilling Company, a Cayman Islands exempted company (“Parent”), as a guarantor, PT. Vantage Drilling Company Indonesia, a company organized under the laws of Indonesia (the “Additional Guarantor”), the other existing guarantors to the Indenture (as defined below) (the “Existing Guarantors”, together with Parent and the Additional Guarantor, the “Guarantors”) and Wells Fargo Bank, National Association, and any and all successors thereto, as trustee (in such capacity, the “Trustee”) and as collateral agent (in such capacity, the “Noteholder Collateral Agent”).

WHEREAS, the Company, the Guarantors and the Trustee and Noteholder Collateral Agent have executed and delivered that certain Indenture dated as of July 30, 2010 (the “Original Indenture”), providing for the issuance of the Company’s 11 ¹/₂% Senior Secured First Lien Notes due 2015 (the “Notes”), as amended by the First Supplemental Indenture dated as of May 20, 2011 (the “First Supplemental Indenture”), the Second Supplemental Indenture dated as of June 1, 2011 (the “Second Supplemental Indenture”), the Third Supplemental Indenture dated as of June 29, 2011 (the “Third Supplemental Indenture”), the Fourth Supplemental Indenture dated as of April 2, 2012 (the “Fourth Supplemental Indenture”), the Fifth Supplemental Indenture dated as of April 20, 2012 (the “Fifth Supplemental Indenture”), the Sixth Supplemental Indenture dated as of October 25, 2012 (the “Sixth Supplemental Indenture” and together with the Original Indenture, First Supplemental Indenture, Second Supplemental Indenture, Third Supplemental Indenture, Fourth Supplemental Indenture and Fifth Supplemental Indenture, the “Indenture”);

WHEREAS, Section 9.01 of the Indenture provides that the Indenture or the Notes may be amended without the consent of any Holder to, among other things, cure any ambiguity, defect or inconsistency;

WHEREAS, the Indenture provides that under certain circumstances certain Subsidiaries of Parent or the Company will be required to become a guarantor under the Indenture and that such additional guarantors will, among other things execute and deliver to the Trustee a supplemental indenture and Note Guarantee pursuant to which each such additional guarantor shall unconditionally guarantee all of the Company’s Obligations under the Notes and the Indenture on the terms and conditions set forth herein and therein;

WHEREAS, pursuant to Sections 9.01 and 9.06 of the Indenture, the Trustee and Noteholder Collateral Agent is authorized to execute and deliver this Supplemental Indenture; and

WHEREAS, the Company desires to enter into, and, pursuant to the foregoing authority, has requested the Trustee and Noteholder Collateral Agent to join with it and the Guarantors in entering into, this Supplemental Indenture for the purpose of amending the Indenture and the Notes in certain respects as permitted by Section 9.01 of the Indenture (the “Proposed Amendments”).

NOW, THEREFORE, in consideration of the above premises, each party hereby agrees, for the benefit of the others and for the equal and ratable benefit of the Holders, as follows:

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ARTICLE I

AMENDMENTS TO THE INDENTURE AND THE NOTES

Section 1.1 Amendments to the Indenture and Notes. The Indenture and the Notes are hereby amended by:

(a) amending and restating the next to last sentence of Section 4.14(b) as follows: “Parent or the Company shall be required to designate each applicable Subsidiary to become a Restricted Subsidiary and a Guarantor and pledge its assets and property as Collateral pursuant to Section 4.13 (“Additional Note Guarantees”) and shall be required to comply with the conditions set forth in this clause (b) of this Section 4.14 in connection therewith within the time period set forth in Section 4.13.”

(b) amending Section 12.08(b) to replace “not later than 10 Business Days after the date of such Contract Winning Trigger” with “within the time period set forth in Section 4.13 (“Additional Note Guarantees”).

Section 1.2 Additional Amendments. Any and all additional provisions of the Indenture and the Notes are hereby deemed to be amended to reflect the intentions of the amendments provided for in this Article I.

ARTICLE II

ADDITIONAL GUARANTORS

Section 2.1 Agreement to Guarantee. The Additional Guarantor hereby agrees to provide an unconditional Note Guarantee on the terms and subject to the conditions set forth in the Note Guarantee and the Indenture (as amended hereby), including but not limited to Section 4.13 and Article 11 thereof, and subject to the limitations therein.

ARTICLE III

MISCELLANEOUS PROVISIONS

Section 3.1 Defined Terms. For all purposes of this Supplemental Indenture, except as otherwise defined or unless the context otherwise requires, terms used in capitalized form in this Supplemental Indenture and defined in the Indenture have the meanings specified in the Indenture.

Section 3.2 Indenture. Except as expressly amended hereby, the Indenture and the Notes are in all respects ratified and confirmed and all the terms shall remain in full force and effect. This Supplemental Indenture shall form a part of the Indenture for all purposes, and every Holder heretofore or hereafter authenticated and delivered under the Indenture shall be bound hereby and all terms and conditions of both shall be read together as though they constitute a single instrument.

Section 3.3 Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

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Section 3.4 Successors. All agreements of the Company and the Guarantors in this Supplemental Indenture and the Notes shall bind their respective successors. All agreements of the Trustee and Noteholder Collateral Agent in this Supplemental Indenture shall bind their successors.

Section 3.5 Duplicate Originals. All parties may sign any number of copies of this Supplemental Indenture. Each signed copy shall be an original, but all of them together shall represent the same agreement. It is the express intent of the parties to be bound by the exchange of signatures on this Supplemental Indenture via telecopy or other form of electronic transmission.

Section 3.6 Severability. In case any one or more of the provisions in this Supplemental Indenture shall be held invalid, illegal or unenforceable, in any respect for any reason, the validity, legality and enforceability of any such provision in every other respect and of the remaining provisions shall not in any way be affected or impaired thereby, it being intended that all of the provisions hereof shall be enforceable to the full extent permitted by law.

Section 3.7 Trustee Disclaimer. The Trustee and Noteholder Collateral Agent accepts the amendments of the Indenture effected by this Supplemental Indenture and agrees to execute the trust created by the Indenture as hereby amended, but on the terms and conditions set forth in the Indenture, including the terms and provisions defining and limiting the liabilities and responsibilities of the Trustee and Noteholder Collateral Agent, which terms and provisions shall in like manner define and limit its liabilities and responsibilities in the performance of the trust created by the Indenture as hereby amended, and without limiting the generality of the foregoing, the Trustee and Noteholder Collateral Agent shall not be responsible in any manner whatsoever for or with respect to any of the recitals or statements contained herein, all of which recitals or statements are made solely by the Company and the Guarantors, and the Trustee and Noteholder Collateral Agent make no representation with respect to any such matters. Additionally, the Trustee and Noteholder Collateral Agent make no representations as to the validity or sufficiency of this Supplemental Indenture.

Section 3.8 Effectiveness. The Proposed Amendments effected by this Supplemental Indenture shall take effect immediately upon the provision by the Company to the Trustee of the Officers’ Certificate and Opinion of Counsel described in Section 9.06 of the Indenture.

Section 3.9 TIA Controls. If any provision of this Supplemental Indenture limits, qualifies or conflicts with another provision that is required to be included in this Supplemental Indenture or the Indenture by the TIA, as in force at the date that this Supplemental Indenture is executed, the provisions required by the TIA shall control.

Section 3.10 Supplemental Indenture Controls. In the event there is any conflict or inconsistency between the Indenture and this Supplemental Indenture, the provisions of this Supplemental Indenture shall control.

Section 3.11 Effect of Headings. The Section headings herein are for convenience only and shall not affect the construction thereof.

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IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the day and year written above.

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