FIRST SUPPLEMENTAL INDENTURE

Exhibit 4.2

FIRST SUPPLEMENTAL INDENTURE

     FIRST SUPPLEMENTAL INDENTURE (this “ Supplemental Indenture ”) dated as of August 28, 2008, among Stone Energy Offshore, L.L.C. (the “ New Subsidiary Guarantor ”), a Delaware limited liability company and subsidiary of Stone Energy Corporation, a Delaware corporation (the “ Company ”), the Company and The Bank of New York Mellon Trust Company, N.A., as successor trustee to JPMorgan Chase Bank, National Association, a national banking association, under the Indenture referred to below (the “ Trustee ”).

WITNESSETH :

     WHEREAS the Company has heretofore executed and delivered to the Trustee an Indenture (the “ Indenture ”) dated as of December 15, 2004, providing for the issuance of an unlimited aggregate principal amount of 6 ³ / 4 % Senior Subordinated Notes due 2014 (the “ Securities ”);

     WHEREAS Section 4.13 of the Indenture provides that under certain circumstances the Company is required to cause the New Subsidiary Guarantor to execute and deliver to the Trustee a supplemental indenture pursuant to which the New Subsidiary Guarantor shall unconditionally guarantee all the Company’s obligations under the Securities pursuant to a Subsidiary Guaranty on the terms and conditions set forth herein; and

     WHEREAS pursuant to Section 9.01 of the Indenture, the Trustee and the Company are authorized to execute and deliver this Supplemental Indenture;

     NOW THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby