Exhibit 4.2

OFFSHORE GROUP INVESTMENT LIMITED

AND EACH OF THE GUARANTORS PARTY HERETO

11 ¹/2% SENIOR SECURED FIRST LIEN NOTES DUE 2015

FIRST SUPPLEMENTAL INDENTURE

Dated as of May 20, 2011

Wells Fargo Bank, National Association,

as Trustee and Noteholder Collateral Agent

THIS FIRST SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of May 20, 2011, is by and among Offshore Group Investment Limited, a Cayman Islands exempted company (the “Company”), Vantage Drilling Company, a Cayman Islands exempted company (“Parent”), as a Guarantor, the other Guarantors (as defined in the Indenture referred to herein) and Wells Fargo Bank, National Association, and any and all successors thereto, as trustee (in such capacity, the “Trustee”) and as collateral agent (in such capacity, the “Noteholder Collateral Agent”).

WHEREAS, the Company, the Guarantors and the Trustee and Noteholder Collateral Agent have executed and delivered that certain Indenture dated as of July 30, 2010 (the “Indenture”), providing for the issuance of the Company’s 11 ¹/2% Senior Secured First Lien Notes due 2015 (the “Notes”);

WHEREAS, Section 9.01 of the Indenture provides that the Indenture or the Notes may be amended without the consent of any Holder to, among other things, cure any ambiguity, defect or inconsistency;

WHEREAS, Section 9.02 of the Indenture provides that the Indenture or the Notes may be amended with the consent of Holders representing at least a majority in principal amount of the Notes then outstanding (including, without limitation, consents obtained in connection with a purchase of, or tender offer or exchange offer for, Notes);

WHEREAS, the Company has solicited consents, as required by Section 9.02 of the Indenture, from the Holders for certain proposed amendments (the “Proposed Amendments”) to the Indenture and the Notes pursuant to the Consent Solicitation Statement dated May 11, 2011 (as the same may be amended or supplemented from time to time, the “Statement”), which Proposed Amendments are contained in this Supplemental Indenture;

WHEREAS, (i) the Company has received the written consent of the Holders of more than a majority in principal amount of the outstanding Notes to the Proposed Amendments, all as certified by an Officers’ Certificate delivered to the Trustee simultaneously with the execution and delivery of this Supplemental Indenture, (ii) the Company has delivered to the Trustee and Noteholder Collateral Agent simultaneously with the execution and delivery of this Supplemental Indenture an Opinion of Counsel relating to this Supplemental Indenture as contemplated by Sections 9.06, 13.04 and 13.05 of the Indenture and (iii) the Company and the Guarantors have satisfied, performed and complied with all other conditions required under Article 9 of the Indenture to enable the Company, the Guarantors and the Trustee and Noteholder Collateral Agent to enter into this Supplemental Indenture and to make this Supplemental Indenture a valid and binding agreement of the Issuer and the Guarantors;

WHEREAS, pursuant to Sections 9.01, 9.02 and 9.06 of the Indenture, the Trustee and Noteholder Collateral Agent is authorized to execute and deliver this Supplemental Indenture; and

WHEREAS, the Company desires to enter into, and, pursuant to the foregoing authority, has requested the Trustee and Noteholder Collateral Agent to join with it and the Guarantors in entering into, this Supplemental Indenture for the purpose of amending the Indenture and the Notes in certain respects as permitted by Sections 9.01 and 9.02 of the 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, as follows:

ARTICLE I

AMENDMENTS TO THE INDENTURE AND THE NOTES

Section 1.1 Amendments to the Indenture and Notes. The Indenture and the Notes are hereby amended by:

(a) amending Section 1.01 to add the definition of “Acquisitions” as follows:

“ “Acquisitions” means the acquisition by the Company from Parent of (i) all of the equity interests of P2020 Rig Co., a wholly owned subsidiary of Parent, and (ii) all of the equity interests of Vantage Holdings Malaysia I Co., a wholly owned subsidiary of Parent, and each of its wholly owned subsidiaries.”

(b) amending the definition of “Applicable Premium” in Section 1.01 to capitalize the term “Treasury Rate” and to add to the end of the definition a new paragraph as follows:

“The Company will calculate the Applicable Premium prior to the applicable redemption date and deliver an officers’ certificate setting forth the Applicable Premium and showing the calculation thereof in reasonable detail.”

(c) amending and restating the definition of “Security Agreement” in Section 1.01 to read as follows:

““Security Agreement” means the Pledge and Security Agreement, dated as of July 30, 2010, among the Company and the Grantors (as defined in the Pledge and Security Agreement) from time to time party thereto in favor of the Noteholder Collateral Agent, as amended, amended and restated, or supplemented from time to time in accordance with its terms.”

(d) amending Section 1.01 to add the definition of “Treasury Rate” as follows:

““Treasury Rate” means, as of any redemption date, the yield to maturity as of such redemption date of United States Treasury securities with a constant maturity (as compiled and published in the most recent Federal Reserve Statistical Release H.15 (519) that has become publicly available at least two business days prior to the redemption date (or, if such Statistical Release is no longer published, any publicly available source of similar market data)) most nearly equal to the period from the redemption date to February 1, 2013; provided, however, that if the period from the redemption date to February 1, 2013 is less than one year, the weekly average yield on actually traded United States Treasury securities adjusted to a constant maturity of one year will be used.”

(e) amending and restating Section 4.08(b)(1) to read:

“the incurrence by the Company and the Guarantors of (a) (i) additional Indebtedness and letters of credit under a Credit Agreement (with letters of credit being deemed to have a principal amount equal to the maximum potential liability of the Company and the Guarantors thereunder) and (ii) Additional Notes and related Note Guarantees issued under this Indenture in a maximum aggregate principal amount at any one time outstanding under this clause (1)(a) not to exceed $25.0 million and (b) additional Indebtedness represented by Additional Notes and related Note Guarantees or substantially similar securities with the same or different CUSIP number as the Initial Notes to fund the Acquisitions not to exceed $225.0 million in aggregate principal amount;”

(f) amending Section 4.08(b) to:

(i) add a new subsection (15) as follows:

“(15) the incurrence, from time to time in one or more offerings, by Parent of up to $125,000,000 aggregate principal amount of Indebtedness convertible into ordinary shares of Parent, the proceeds of which will be used to invest in Parent’s business.”

(ii) delete “and” from the end of subsection (13); and

(iii) replace “.” with “; and” at the end of subsection (14).

(g) amending Section 4.11(b) to

(i) delete the word “and” at the end of subsection (9);

(ii) add a new subsection (10) as follows:

“(10) the Acquisitions; and” and

(iii) renumber the existing subsection (10) as subsection (11).

(h) amending Section 4.16 to add Section 4.16(d) and (e) to read as follows:

“(d) Delivery of such reports, information and documents to the Trustee shall be for informational purposes only, and the Trustee’s receipt thereof shall not constitute constructive notice of any information contained therein or determinable from information contained therein, including Parent or the Company, compliance with any of their covenants hereunder (as to which the Trustee is entitled to rely exclusively on officers’ certificates).

(e) Documents filed by us with the SEC via the EDGAR system will be deemed filed with the Trustee as of the time such documents are filed via EDGAR. Delivery of such reports, information and documents to the Trustee is for informational purposes only, and the Trustee’s receipt of such shall not constitute constructive notice of any information contained therein or determinable from information contained therein, including the Company’s compliance with any of their covenants hereunder (as to which the Trustee is entitled to rely exclusively on officers’ certificates).”

Section 1.2 Additional Amendments. Any and all additional provisions of the Indenture and the Notes are hereby deemed to be amended to reflect the intentions of the amendments provided for in this Article I.

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 expressly 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 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.

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 Guarantors in this Supplemental Indenture and the Notes shall bind their respective successors. All agreements of the Trustee and Noteholder Collateral Agent in this Supplemental Indenture shall bind their 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 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 and Noteholder Collateral Agent 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 and Noteholder Collateral Agent, 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 and Noteholder Collateral Agent 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 Guarantors, and the Trustee and Noteholder Collateral Agent make no representation with respect to any such matters. Additionally, the Trustee and Noteholder Collateral Agent make no representations as to the validity or sufficiency of this Supplemental Indenture.

Section 2.8 Effectiveness. The Proposed Amendments effected by this Supplemental Indenture shall take effect immediately upon the provision by the Company to the Trustee of an Officers’ Certificate certifying that the conditions set forth in the Company’s Consent Solicitation Statement dated May 11, 2011, as amended or supplemented from time to time, have been either satisfied or, where permitted, waived by the Company.

Section 2.9 Supplemental Indenture Controls. In the event there is any conflict or inconsistency between the Indenture and this Supplemental Indenture, the provisions of this Supplemental Indenture shall control.

Section 2.10 Effect of Headings. The Section headings herein are for convenience only and shall not affect the construction thereof.

[THE REMAINDER OF THIS PAGE IS INTENTIONALLY LEFT BLANK]

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the day and year written above.

[Signature Page to First Supplemental Indenture]

[Signature Page to First Supplemental Indenture]

[Signature Page to First Supplemental Indenture]

[Signature Page to First Supplemental Indenture]