SECOND SUPPLEMENTAL INDENTURE Dated as of November 6, 2012 to INDENTURE Dated as of December 15, 2004 Among STONE ENERGY CORPORATION as Issuer, The GUARANTOR named therein and THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A. as Trustee 6.75% SeniorSubordinated Notes due 2014 SECOND SUPPLEMENTAL INDENTURE

Exhibit 4.1

EXECUTION VERSION

SECOND SUPPLEMENTAL INDENTURE

Dated as of November 6, 2012

to

INDENTURE

Dated as of December 15, 2004

Among

STONE ENERGY CORPORATION

as Issuer,

The GUARANTOR named therein

and

THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A.

as Trustee

6.75% Senior Subordinated Notes due 2014

SECOND SUPPLEMENTAL INDENTURE

SECOND SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of November 6, 2012, by and among Stone Energy Corporation, a Delaware corporation (the “Company”), Stone Energy Offshore, L.L.C., a Delaware limited liability company (the “Guarantor”), and The Bank of New York Mellon Trust Company, N.A., as trustee under the Indenture referred to below (the “Trustee”).

RECITALS

WHEREAS the Company has heretofore executed and delivered to the Trustee an Indenture (as such may be amended from time to time, the “Indenture”), dated as of December 15, 2004, providing for the issuance of its 6.75% Senior Subordinated Notes due 2014 (the “Notes”);

WHEREAS, on or about December 15, 2004, the Company issued $200,000,000 aggregate principal amount of Notes, all of which Notes are currently outstanding;

WHEREAS, Section 9.02 of the Indenture provides that, with the consent of Holders representing at least a majority in principal amount of the outstanding Notes, the Company, the Guarantor and the Trustee may enter into an indenture supplemental to the Indenture for the purpose of amending the Indenture or the Notes (subject to certain exceptions);

WHEREAS, the Company desires and has requested the Trustee to join with it and the Guarantor in entering into this Supplemental Indenture for the purpose of amending the Indenture and the Notes in certain respects as permitted by Section 9.02 of the Indenture;

WHEREAS, the Company has been soliciting consents to this Supplemental Indenture upon the terms and subject to the conditions set forth in its Offer to Purchase and Consent Solicitation Statement dated October 22, 2012 and the related consent and letter of transmittal (which together, including any amendments, modifications or supplements thereto, constitute the “Tender Offer”);

WHEREAS, (1) the Company has received the consent of the Holders of at least a majority in principal amount of the outstanding Notes, all as certified by an Officers’ Certificate delivered to the Trustee simultaneously with the execution and delivery of this Supplemental Indenture, (2) the Company has delivered to the Trustee simultaneously with the execution and delivery of this Supplemental Indenture an Opinion of Counsel relating to this Supplemental Indenture as contemplated by Section 9.06 of the Indenture and (3) the Company and the Guarantor have satisfied all other conditions required under Article 9 of the Indenture to enable the Company, the Guarantor and the Trustee to enter into this Supplemental Indenture.

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 of the Notes, as follows:

ARTICLE I

AMENDMENTS TO INDENTURE AND NOTES

Section 1.1 Amendment.

(a) The Indenture is hereby amended by deleting in their entireties Sections 4.02, 4.03, 4.04, 4.05, 4.06, 4.07, 4.09, 4.10, 4.11 (except for the last sentence thereof), 4.12, 4.13, 4.14, 4.15, 6.01(5), 6.01(6), 6.01(7), 6.01(8) and 6.01(9) and Article 5 (except for Sections 5.01(i) and 5.02(a)) of the Indenture.

(b) Effective as of the date hereof, none of the Company, the Guarantor, the Trustee or other parties to or beneficiaries of the Indenture shall have any rights, obligations or liabilities under such Sections or Article and such Sections or Article shall not be considered in determining whether an Event of Default has occurred or whether the Company has observed, performed or complied with the provisions of the Indenture.

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Section 1.2 Amendments of Definitions and Notes. The Indenture is hereby amended by deleting any definitions from the Indenture with respect to which references would be eliminated as a result of the amendments of the Indenture pursuant to Section 1.1 hereof, and the Notes are hereby deemed to be amended to delete all provisions inconsistent with the Indenture that is effected by such amendments.

ARTICLE II

MISCELLANEOUS PROVISIONS

Section 2.1 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 2.2 Indenture. Except as 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 of Notes 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, except that in the case of conflict the provisions of this Supplemental Indenture shall control.

Section 2.3 Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

Section 2.4 Successors. All agreements of the Company and the Guarantor in this Supplemental Indenture and the Notes shall bind their respective successors. All agreements of the Trustee in this Supplemental Indenture shall bind its successors.

Section 2.5 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 2.6 Severability. In case any one or more of the provisions in this Supplemental Indenture or in the Notes 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 2.7 Trustee Disclaimer. The Trustee 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, 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 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 Guarantor, and the Trustee makes no representation with respect to any such matters. Additionally, the Trustee makes no representations as to the validity or sufficiency of this Supplemental Indenture.

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Section 2.8 Effectiveness. The provisions of this Supplemental Indenture shall be effective only upon execution and delivery of this instrument by the parties hereto. Notwithstanding the foregoing sentence, the provisions of this Supplemental Indenture shall become operative only upon the purchase by the Company of at least a majority in principal amount of the outstanding Notes pursuant to the Tender Offer, with the result that the amendments to the Indenture effected by this Supplemental Indenture shall be deemed to be revoked retroactive to the date hereof if such purchase shall not occur. The Company shall notify the Trustee promptly after the occurrence of such purchase or promptly after the Company shall determine that such purchase will not occur.

Section 2.9 Endorsement and Change of Form of Notes. Any Notes authenticated and delivered after the close of business on the date that this Supplemental Indenture becomes operative in substitution for Notes then outstanding and all Notes presented or delivered to the Trustee on and after that date for such purpose shall be stamped, imprinted or otherwise legended by the Company, with a notation as follows:

“Effective as of November 6, 2012, the Company has amended the Indenture, as provided in the Second Supplemental Indenture, dated as of November 6, 2012. Reference is hereby made to said Second Supplemental Indenture, copies of which are on file with the Trustee, for a description of the amendments made therein.”

Section 2.10 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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