Exhibit 3.1

CERTIFICATE OF DESIGNATIONS

OF

SERIES C JUNIOR PARTICIPATING PREFERRED SHARES

OF

ENERGY XXI LTD

ENERGY XXI LTD, a Bermuda exempted company (the “Company”), certifies that pursuant to the authority contained in Bye-Law 5 of its Bye-Laws, the Board of Directors of the Company (the “Board”), by resolution adopted by unanimous written consent, on February 15, 2016, duly approved and adopted the following resolution, which resolution remains in full force and effect on the date hereof:

RESOLVED, that a series of preferred shares, par value $0.01 per share, of the Company be, and hereby are, created, and that the designation and number of shares thereof and the voting and other powers, preferences, and relative, participating, optional or other rights of the shares of such series and the qualifications, limitations and restrictions thereof are as set forth below and in the Memorandum of Association of the Company (“Memorandum of Association”) and the Bye-laws of the Company (“Bye-laws”):

Series C Junior Participating Preferred Shares

(1) Designation and Amount. The shares of such series shall be designated as “Series C Junior Participating Preferred Shares” (the “Series C Preferred Shares”) and the number of shares constituting the Series C Preferred Shares shall be 150,000. Subject to the Company’s Bye-laws, such number of shares may be increased or decreased by resolution of the Board; provided, that no decrease shall reduce the number of Series C Preferred Shares to a number less than the number of shares then issued and outstanding plus the number of shares reserved for issuance upon the exercise of outstanding options, rights or warrants or upon the conversion of any outstanding securities issued by the Company convertible into Series C Preferred Shares.

(2) Dividends and Distributions.

(a) Subject to the rights of the holders of any shares of any series of Preferred Shares (or any similar shares) ranking prior and superior to the Series C Preferred Shares with respect to dividends, the holders of shares of Series C Preferred Shares, in preference to the holders of common shares, par value $0.005 per share (the “Common Shares”), of the Company, and of any other junior shares, shall be entitled to receive, when, as and if declared by the Board out of funds legally available for the purpose and in accordance with the Companies Act 1981 of Bermuda, the Bye-laws, the Memorandum of Association or otherwise, quarterly dividends payable in cash on the first day of March, June, September and December in each year (each such date being referred to herein as a “Quarterly Dividend Payment Date”), commencing on the first Quarterly Dividend Payment Date after the first issuance of Series C Preferred Shares (or fraction thereof), in an amount per share (rounded to the nearest cent) equal to the greater of (1) $1.00 or (2) subject to the provision for adjustment hereinafter set forth, 1,000 times the aggregate per share amount of all cash dividends, and 1,000 times the aggregate per share amount (payable in kind) of all non-cash dividends or other distributions, other than a dividend payable in Common Shares or a subdivision of the outstanding Common Shares (by reclassification or otherwise), declared on the Common Shares since the immediately preceding Quarterly Dividend Payment Date or, with respect to the first Quarterly Dividend Payment Date, since the first issuance of any share or fraction of a share of Series C Preferred Shares. In the event the Company shall at any time declare or pay any dividend on the Common Shares payable in Common Shares, or effect a subdivision or combination or consolidation of the outstanding Common Shares (by reclassification or otherwise than by payment of a dividend in Common Shares) into a greater or lesser number of Common Shares, then in each such case the amount to which holders of Series C Preferred Shares were entitled immediately prior to such event under clause (2) of the preceding sentence shall be adjusted by multiplying such amount by a fraction, the numerator of which is the number of Common Shares outstanding immediately after such event and the denominator of which is the number of Common Shares that were outstanding immediately prior to such event.

(b) The Company shall declare a dividend distribution on the Series C Preferred Shares as provided in paragraph (a) of this subsection immediately after it declares a dividend or distribution on the Common Shares (other than a dividend payable in Common Shares); provided, that in the event no dividend or distribution shall have been declared on the Common Shares during the period between any Quarterly Dividend Payment Date and the next subsequent Quarterly Dividend Payment Date, a dividend of $1.00 per share on the Series C Preferred Shares shall nevertheless be payable on such subsequent Quarterly Dividend Payment Date.

(c) Dividends shall begin to accrue and be cumulative on issued and outstanding Series C Preferred Shares from the Quarterly Dividend Payment Date next preceding the date of issue of such shares, unless the date of issue of such shares is prior to the record date for the first Quarterly Dividend Payment Date, in which case dividends on such shares shall begin to accrue from the date of issue of such shares, or unless the date of issue is a Quarterly Dividend Payment Date or is a date after the record date for the determination of holders of Series C Preferred Shares entitled to receive a quarterly dividend and before such Quarterly Dividend Payment Date, in either of which events such dividends shall begin to accrue and be cumulative from such Quarterly Dividend Payment Date. Accrued but unpaid dividends on the Series C Preferred Shares shall only be paid if and when they are permitted to be paid under the terms of each of the Company’s 7.25% Convertible Perpetual Preferred Shares and 5.625% Convertible Perpetual Preferred Shares. Accrued but unpaid dividends shall not bear interest. Dividends paid on the Series C Preferred Shares in an amount less than the total amount of such dividends at the time accrued and payable on such shares shall be allocated pro rata on a share-by-share basis among all such shares at the time issued and outstanding. The Board may fix a record date for the determination of holders of Series C Preferred Shares entitled to receive payment of a dividend or distribution declared thereon, which record date shall be not more than sixty (60) days prior to the date fixed for the payment thereof.

(3) Voting Rights. The holders of Series C Preferred Shares shall have the following voting rights:

(a) Subject to the provision for adjustment hereinafter set forth, each share of Series C Preferred Shares shall entitle the holder thereof to 1,000 votes on all matters submitted to a vote of the shareholders of the Company. In the event the Company shall at any time declare or pay any dividend on the Common Shares payable in Common Shares, or effect a subdivision or combination or consolidation of the outstanding Common Shares (by reclassification or otherwise than by payment of a dividend in Common Shares) into a greater or lesser number of Common Shares, then in each such case the number of votes per share to which holders of Series C Preferred Shares were entitled immediately prior to such event shall be adjusted by multiplying such number by a fraction, the numerator of which is the number of Common Shares outstanding immediately after such event and the denominator of which is the number of Common Shares that were outstanding immediately prior to such event.

(b) Except as otherwise provided herein, in any other certificate of designation creating a series of Preferred Shares or any similar shares, or by law, the holders of Series C Preferred Shares and the holders of Common Shares and any other shares in the capital of the Company having general voting rights shall vote together as one class on all matters submitted to a vote of shareholders of the Company.

(c) Except as set forth herein, or as otherwise provided by law, holders of Series C Preferred Shares shall have no special voting rights and their consent shall not be required (except to the extent they are entitled to vote with holders of Common Shares as set forth herein) for taking any corporate action.

(4) Certain Restrictions.

(a) Whenever quarterly dividends or other dividends or distributions payable on the Series C Preferred Shares as provided in Section (2) are in arrears, thereafter and until all accrued and unpaid dividends and distributions, whether or not declared, on Series C Preferred Shares issued and outstanding shall have been paid in full, the Company shall not:

(1) declare or pay dividends, or make any other distributions, on any shares ranking junior (either as to dividends or upon liquidation, dissolution or winding up) to the Series C Preferred Shares;

(2) declare or pay dividends, or make any other distributions, on any shares ranking on a parity (either as to dividends or upon liquidation, dissolution or winding up) with the Series C Preferred Shares, except dividends paid ratably on the Series C Preferred Shares and all such parity shares on which dividends are payable or in arrears in proportion to the total amounts to which the holders of all such shares are then entitled;

(3) redeem or purchase or otherwise acquire for consideration shares ranking junior (either as to dividends or upon liquidation, dissolution or winding up) to the Series C Preferred Shares other than (A) such redemptions or purchases that may be deemed to occur upon the exercise of share options, warrants or similar rights or grant, vesting or lapse of restrictions on the grant of any other performance shares, restricted shares, restricted share units or other equity awards to the extent that such shares represent all or a portion of (x) the exercise or purchase price of such options, warrants or similar rights or other equity awards and (y) the amount of withholding taxes owed by the recipient of such award in respect of such grant, exercise, vesting or lapse of restrictions; (B) the repurchase, redemption, or other acquisition or retirement for value of any such shares from employees, former employees, directors, former directors, consultants or former consultants of the Company or their respective estate, spouse, former spouse or family member, pursuant to the terms of the agreements pursuant to which such shares were acquired, provided that the Company may at any time redeem, purchase or otherwise acquire shares of any such junior shares in exchange for shares of the Company ranking junior (either as to dividends or upon dissolution, liquidation or winding up) to the Series C Preferred Shares; or

(4) redeem or purchase or otherwise acquire for consideration any Series C Preferred Shares, or any shares ranking on a parity with the Series C Preferred Shares, except in accordance with a purchase offer made in writing or by publication (as determined by the Board) to all holders of such shares upon such terms as the Board, after consideration of the respective annual dividend rates and other relative rights and preferences of the respective series and classes, shall determine in good faith will result in fair and equitable treatment among the respective series or classes.

(b) The Company shall not permit any subsidiary of the Company to purchase or otherwise acquire for consideration any shares of the Company unless the Company could, under paragraph (a) of this Section (4), purchase or otherwise acquire such shares at such time and in such manner.

(5) Reacquired Shares. Any Series C Preferred Shares purchased or otherwise acquired by the Company in any manner whatsoever shall be cancelled promptly after the acquisition thereof. All such shares shall upon their cancellation become authorized but unissued Preferred Shares and may be reissued as part of a new series of Preferred Shares subject to the conditions and restrictions on issuance set forth herein, in the Memorandum of Association and/or the Bye-laws, or in any other certificate of designation creating a series of Preferred Shares or any similar shares or as otherwise required by law.

(6) Liquidation, Dissolution or Winding Up. Upon any liquidation, dissolution or winding up of the Company, voluntary or otherwise, no distribution shall be made (1) to the holders of shares ranking junior (either as to dividends or upon liquidation, dissolution or winding up) to the Series C Preferred Shares unless, prior thereto, the holders of Series C Preferred Shares shall have received the greater of (A) $1,000 per share, plus an amount equal to accrued and unpaid dividends and distributions thereon, whether or not declared, to the date of such payment, and (B) an amount, subject to the provision for adjustment hereinafter set forth, equal to 1,000 times the aggregate amount to be distributed per share to holders of Common Shares, or (2) to the holders of shares ranking on a parity (either as to dividends or upon liquidation, dissolution or winding up) with the Series C Preferred Shares, except distributions made ratably on the Series C Preferred Shares and all such parity shares in proportion to the total amounts to which the holders of all such shares are entitled upon such liquidation, dissolution or winding up. In the event the Company shall at any time declare or pay any dividend on the Common Shares payable in Common Shares, or effect a subdivision or combination or consolidation of the outstanding Common Shares (by reclassification or otherwise than by payment of a dividend in Common Shares) into a greater or lesser number of Common Shares, then in each such case the aggregate amount to which holders of Series C Preferred Shares were entitled immediately prior to such event under the proviso in clause (1) of the preceding sentence shall be adjusted by multiplying such amount by a fraction, the numerator of which is the number of Common Shares outstanding immediately after such event and the denominator of which is the number of Common Shares that were outstanding immediately prior to such event.

(7) Consolidation, Merger, Etc. In case the Company shall enter into any consolidation, amalgamation, merger, combination or other transaction in which the Common Shares are exchanged for or changed into other shares or securities, cash and/or any other property, then in any such case each Series C Preferred Share shall at the same time be similarly exchanged or changed into an amount per share, subject to the provision for adjustment hereinafter set forth, equal to 1,000 times the aggregate amount of shares, securities, cash and/or any other property (payable in kind), as the case may be, into which or for which each Common Share is changed or exchanged. In the event the Company shall at any time declare or pay any dividend on the Common Shares payable in Common Shares, or effect a subdivision or combination or consolidation of the outstanding Common Shares (by reclassification or otherwise than by payment of a dividend in Common Shares) into a greater or lesser number of Common Shares, then in each such case the amount set forth in the preceding sentence with respect to the exchange or change of Series C Preferred Shares shall be adjusted by multiplying such amount by a fraction, the numerator of which is the number of Common Shares outstanding immediately after such event and the denominator of which is the number of Common Shares that were outstanding immediately prior to such event.

(8) No Redemption. The Series C Preferred Shares shall not be redeemable.

(9) Rank. The Series C Preferred Shares shall rank, with respect to the payment of dividends and the distribution of assets, junior to all series of any other class of the Company’s Preferred Shares (including, for the avoidance of doubt, junior to any outstanding shares of the Company’s 7.25% Convertible Perpetual Preferred Stock and 5.625% Convertible Perpetual Preferred Stock), and shall rank senior to the Common Shares as to such matters.

(10) Amendment. The Memorandum of Association and the Bye-laws of the Company shall not be amended in any manner which would materially alter or change the powers, preferences or special rights of the Series C Preferred Shares so as to affect them adversely without the affirmative vote of the holders of at least two-thirds of the outstanding shares of Series C Preferred Shares, voting together as a single class.

(11) Fractional Shares. The Series C Preferred Shares may be issued in fractions of a share, which fractions shall entitle the holder, in proportion to such holder’s fractional shares, to exercise voting rights, receive dividends, participate in distributions, and to have the benefit of all other rights of holders of Series C Preferred Shares.

IN WITNESS WHEREOF, Energy XXI Ltd has caused this certificate to be executed on behalf of the Company by the undersigned authorized officer this 15th day of February, 2016.