THIRD SUPPLEMENTAL INDENTURE DATED AS OF MAY 8, 2006

Exhibit 4.13.1

CHESAPEAKE ENERGY CORPORATION

and

the Subsidiary Guarantors named herein

2.75% CONTIGENT CONVERTIBLE SENIOR NOTES DUE 2035

THIRD SUPPLEMENTAL INDENTURE

DATED AS OF MAY 8, 0000

XXX XXXX XX XXX XXXX TRUST COMPANY, N.A.

as Trustee

THIS THIRD SUPPLEMENTAL INDENTURE, dated as of May 8, 2006, is among Chesapeake Energy Corporation, an Oklahoma corporation (the “Company”), each of the parties identified under the caption “Subsidiary Guarantors” on the signature page hereto (the “Subsidiary Guarantors”) and The Bank of New York Trust Company, N.A., as Trustee.

RECITALS

WHEREAS, the Company, the Subsidiary Guarantors a party thereto and the Trustee entered into an Indenture, dated as of November 8, 2005, (the “Indenture”), pursuant to which the Company has originally issued $690,000,000 in principal amount of 2.75% Contingent Convertible Senior Notes due 2035 (the “Notes”); and

WHEREAS, Section 10.01(3) of the Indenture provides that the Company, the Subsidiary Guarantors and the Trustee may amend or supplement the Indenture without notice to or consent of any Holder to reflect the release of any Subsidiary Guarantor, as provided for in the Indenture; and

WHEREAS, the Company has taken all actions required to effect the release, pursuant to Sections 11.02 and 11.04 of the Indenture, of Oxley Petroleum Co. (“Oxley”), an Oklahoma limited partnership.

WHEREAS, all acts and things prescribed by the Indenture, by law and by the charter and the bylaws (or comparable constituent documents) of the Company, of the Subsidiary Guarantors and of the Trustee necessary to make this Third Supplemental Indenture a valid instrument legally binding on the Company, the Subsidiary Guarantors and the Trustee, in accordance with its terms, have been duly done and performed;

NOW, THEREFORE, to comply with the provisions of the Indenture and in consideration of the above premises, the Company, the Subsidiary Guarantors and the Trustee covenant and agree for the equal and proportionate benefit of the respective Holders of the Notes as follows:

ARTICLE 1

Section 1.01. This Third Supplemental Indenture is supplemental to the Indenture and does and shall be deemed to form a part of, and shall be construed in connection with and as part of, the Indenture for any and all purposes.

Section 1.02. This Third Supplemental Indenture shall become effective immediately upon its execution and delivery by each of the Company, the Subsidiary Guarantors and the Trustee.

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ARTICLE 2

Section 2.01. As a result of the dissolution of Oxley, the Company has taken all actions required to effect the release, pursuant to Section 11.04 of the Indenture, of Oxley as a Subsidiary Guarantor. The notation on the Securities relating to the Guarantee shall be deemed to exclude the name of Oxley and the signature of an Officer of Oxley on its behalf.

ARTICLE 3

Section 3.01. Except as specifically modified herein, the Indenture and the Notes are in all respects ratified and confirmed (mutatis mutandis) and shall remain in full force and effect in accordance with their terms with all capitalized terms used herein without definition having the same respective meanings ascribed to them as in the Indenture.

Section 3.02. Except as otherwise expressly provided herein, no duties, responsibilities or liabilities are assumed, or shall be construed to be assumed, by the Trustee by reason of this Third Supplemental Indenture. This Third Supplemental Indenture is executed and accepted by the Trustee subject to all the terms and conditions set forth in the Indenture with the same force and effect as if those terms and conditions were repeated at length herein and made applicable to the Trustee with respect hereto.

Section 3.03. THE LAW OF THE STATE OF NEW YORK SHALL GOVERN AND BE USED TO CONSTRUE AND ENFORCE THIS THIRD SUPPLEMENTAL INDENTURE.

Section 3.04. The parties may sign any number of copies of this Third Supplemental Indenture. Each signed copy shall be an original, but all of such executed copies together shall represent the same agreement.

[NEXT PAGE IS SIGNATURE PAGE]

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IN WITNESS WHEREOF, the parties hereto have caused this Third Supplemental Indenture to be duly executed, all as of the date first written above.

/s/ Xxxxxx X. XxXxxxxxx

Xxxxxx X. XxXxxxxxx

Chief Executive Officer of the Company and

of the Subsidiaries listed below:

Corporate Subsidiaries:

CHESAPEAKE EAGLE CANADA CORP.

CHESAPEAKE ENERGY LOUISIANA

            CORPORATION

CHESAPEAKE SOUTH TEXAS CORP.

NOMAC DRILLING CORPORATION

XXXXXX HOLDING COMPANY, INC.

XXXXXX OILFIELD COMPANY

XXXXXX TRUCKING COMPANY

NOMAC 100 CORP.

W.W. REALTY, INC.

CHESAPEAKE OPERATING, INC.,

On behalf of itself and, as general partner, the following limited partnerships:

CHESAPEAKE EXPLORATION LIMITED

            PARTNERSHIP

CHESAPEAKE LOUISIANA, L.P.

CHESAPEAKE SIGMA, L.P.

CHESAPEAKE ENERGY MARKETING, INC.,

On behalf of itself and, as general partner, the following limited partnerships:

MIDCON COMPRESSION, L.P.

Limited Liability Company Subsidiaries:

CHESAPEAKE APPALACHIA, L.L.C.

HAWG HAULING & DISPOSAL, L.L.C.

XXXXXX ACQUISITION, L.L.C.

CHESAPEAKE ACQUISITION, L.L.C.

CHESAPEAKE LAND COMPANY, L.L.C.

CHESAPEAKE ORC, L.L.C.

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CHESAPEAKE ROYALTY, L.L.C. GOTHIC PRODUCTION, L.L.C. MC MINERAL COMPANY, L.L.C. XXXXXXXX PROCESSING, L.L.C. TRUSTEE: THE BANK OF NEW YORK TRUST COMPANY, N.A., as Trustee
			By:		/s/ Xxxxx Xxxxxx
			Name:		Xxxxx Xxxxxx
			Title:		Assistant Vice President

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