First Supplemental Indenture

Exhibit 4.1

THE HOUSTON EXPLORATION COMPANY

AND

THE BANK OF NEW YORK,

as Trustee

FIRST SUPPLEMENTAL INDENTURE

Dated as of May 21, 2007

to

Indenture

Dated as of June 10, 2003

7% Senior Subordinated Notes due 2013

     THIS FIRST SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of May 21, 2007, is by and between The Houston Exploration Company, a Delaware corporation (the “Company”), and The Bank of New York, a New York banking corporation, as trustee (the “Trustee”).

     WHEREAS, the Trustee and the Company have heretofore executed and delivered that certain Indenture dated as of June 10, 2003 (as amended, supplemented or otherwise modified from time to time, the “Indenture”), providing for the issuance of the Company’s 7% Senior Subordinated Notes due 2013 (the “Notes”);

     WHEREAS, on June 10, 2003, the Company issued $175,000,000 aggregate principal amount of Restricted Notes (as defined in the Indenture), and it subsequently exchanged all of such Notes for Unrestricted Notes pursuant to the Exchange Offer (as such terms are defined in the Indenture), all of which Unrestricted Notes are currently outstanding;

     WHEREAS, Section 9.2 of the Indenture provides that, with the consent of Holders representing a majority in principal amount of the Notes then outstanding, the Company, and the Trustee may enter into an indenture supplemental to the Indenture for the purpose of amending or supplementing the Indenture or the Notes (subject to certain exceptions);

     WHEREAS, the Company desires and has requested the Trustee to join with it in entering into this Supplemental Indenture for the purpose of amending the Indenture and the Notes in certain respects as permitted by Section 9.2 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 May 2, 2007 (which statement, including any amendments, modifications or supplements thereto, constitutes the “Tender Offer”);

     WHEREAS, there are no Subsidiary Guarantors;

     WHEREAS, pursuant to Section 9.2 of the Indenture, the Company has delivered a request to the Trustee, accompanied by a resolution of its Board of Directors authorizing the execution of this Supplemental Indenture, requesting the Trustee to join with the Company in the execution of this Supplemental Indenture;

     WHEREAS, pursuant to Sections 9.2 and 9.6 of the Indenture, the Board of Directors has authorized and approved this Supplemental Indenture; and

     WHEREAS, (1) the Company has received the consent of the Holders of a majority in principal amount of the outstanding Notes to the substance of this Supplemental Indenture, evidence of which that is satisfactory to the Trustee having been filed therewith, 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 Officers’ Certificate and an Opinion of Counsel relating to this Supplemental Indenture as contemplated by Sections 9.6 and 12.4 of the Indenture and (3) the Company has satisfied all other conditions

Exhibit A

required under the Indenture to enable the Company 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
DEFINITIONS

     Section 1.1 Deletion of Definitions and Related References. Section 1.1 of Article 1 of the Indenture is hereby amended to delete in their entirety all terms and their respective definitions for which all references are eliminated in the Indenture as a result of the amendments set forth in Article II of this Supplemental Indenture.

ARTICLE II
AMENDMENTS TO INDENTURE AND NOTES

     Section 2.1 Amendments to Articles 3, 4, 5, 6 and 9.

          (a) The Indenture is hereby amended by deleting the following Sections or subsections of the Indenture and all references thereto in their entirety:

Sections 4.4, 4.5(b), 4.5(c), 4.6, 4.7, 4.9 through 4.17;
Clauses (i), (iii), (iv) and (vi) of Section 5.1(a);
Section 5.1(b);
Section 6.1(c) through (f) and (i); and
Section 6.12.

          (b) Section 4.8 is revised to read: “Subject to Article 5, the Company shall do or cause to be done all things necessary to preserve and keep in full force and effect its corporate existence.”

          (c) Section 4.5(a) is revised to read: “The Company shall file with the Trustee and the Commission, and transmit to Holders, such information, documents and other reports, and such summaries thereof, as may be required pursuant to the Trust Indenture Act at the times and in the manner provided pursuant to such Act; provided, however, that any such information, documents or reports required to be filed with the Commission pursuant to Section 13 or 15(d) of the Exchange Act shall be filed with the Trustee within 15 days after the same is so required to be filed with the Commission.”

          (d) Section 9.1(b) is hereby amended by deleting the word “corporation” therein.

          (e) Notwithstanding the foregoing provisions of this Section 2.1, all provisions of the Indenture required by the TIA shall remain in full force and effect, including without limitation the obligations of the Company (1) under Section 314(a)(1) of the TIA to file with the Trustee copies of its annual reports and of the information, documents and other reports that the Company is required to file with the Commission pursuant to Section 13 or 15 of the

Exchange Act and (2) under Section 314(a)(4) of the TIA to furnish to the Trustee, not less often than annually, a brief certificate from the principal executive officer, principal financial officer or principal accounting officer as to his or her knowledge of the Company’s compliance with all conditions and covenants under the Indenture, without regard to any period of grace or requirement of notice provided under the Indenture.

     Section 2.2 Amendments to Notes. The Notes are hereby amended to delete all provisions inconsistent with the amendments to the Indenture effected by this Supplemental Indenture, including, without limitation, paragraph 8 and clauses (c), (d), (e), (f) and (i) of paragraph 13 thereof.

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

     Section 3.4 Successors. All agreements of the Company in this Supplemental Indenture and the Notes shall bind its successors. All agreements of the Trustee in this Supplemental Indenture shall bind its 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.

     Section 3.6 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 3.7 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 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.

     Section 3.8 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 acceptance for purchase by the Company of more than 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 never become operative if such acceptance for purchase shall not occur. The Company shall notify the Trustee promptly after the occurrence of such acceptance for purchase or promptly after the Company shall determine that such acceptance for purchase will not occur.

     Section 3.9 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 May 21, 2007, certain restrictive covenants of the Company and certain Events of Default have been eliminated or limited, as provided in the First Supplemental Indenture, dated as of May 21, 2007. Reference is hereby made to said First Supplemental Indenture, copies of which are on file with the Trustee, for a description of the amendments made therein.”

     Section 3.10 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.

		THE HOUSTON EXPLORATION COMPANY
		By: Name:		/s/ ROBERT T. RAY   Robert T. Ray
		Title:		Senior Vice President and Chief Financial Officer
		THE BANK OF NEW YORK, as Trustee
		By: Name:		/s/ BRIAN ECHAUSSE   Brian Echausse
		Title:		Trust Officer