IRREVOCABLE CONTRACTGUARANTEE

Exhibit 10.20

EXECUTION VERSION

IRREVOCABLE CONTRACT GUARANTEE

This Irrevocable Contract Guarantee (this “Guarantee”) is made in favor of ENSCO Offshore Company, a Delaware corporation (the “Contractor”), by each of the following entities: (a) (i) C/R Cobalt Investment Partnership, L.P. (“C/R CIP”); (ii) C/R Energy Coinvestment II, L.P. (“C/R ECII”); (iii) Riverstone Energy Coinvestment III, L.P. (“RECIII”); (iv) C/R Energy III Cobalt Partnership, L.P. (“CIR ECP”); (v) Carlyle/Riverstone Global Energy and Power Fund III, L.P. (C/R GEPF”); and (vi) Carlyle Energy Coinvestment III, L.P. (“CECIII”) and, together with C/R CIP, C/R ECII, RECIII, C/R ECP, and C/R GEPF, “Carlyle/Riverstone”); (b) (i) First Reserve Fund XI, L.P. (“FR XI”), (ii) FR XI Onshore AIV, L.P. (“FR Onshore” and, together with FR XI, “First Reserve”); (c) (i) GS Capital Partners VI Fund, L.P. (“GSCP VI Onshore”); (ii) GS Capital Partners VI Offshore Fund, L.P. (“GSCP VI Offshore”); (iii) GS Capital Partners V Fund, L.P. (“GSCP V Onshore”); and GS Capital Partners V Offshore Fund, L.P. (“GSCP V Offshore and, together with GSCP VI Onshore, GSCP VI Offshore and GSCP V Onshore, “GSCP”); (d) (i) KERN Energy Partners I LP (“KERN I”), (ii) KERN Energy Partners I U.S., LP (“KERN I US”), (iii) KERN Energy Partners II LP (“KERN II”), (iv) KERN Energy Partners II U.S., LP (“KERN II US”), (v) Caisse de Dépôt et Placement du Québec (“Caisse”), and (vi) The Board of Trustees of the Leland Stanford Junior University (“Stanford” and, together with KERN I, KERN I US, KERN II, KERN II US and Caisse, “KERN Partners”; KERN Partners, together with Carlyle/Riverstone, First Reserve, and GSCP, the “Guarantors” and each individual entity listed above a “Guarantor”).

WHEREAS, Contractor is entering into a Offshore Daywork Drilling Contract, dated May 5, 2008 (the “Agreement”; capitalized terms used herein, but not defined, shall have the meanings ascribed to them in the Agreement), with Cobalt International Energy, L.P., a Delaware limited partnership (hereinafter referred to as the “Operator”);

WHEREAS, Contractor is not willing to enter into such Agreement with Operator unless Contractor receives sufficient credit support, collateral and/or other assurance regarding Operator’s ability to fulfill its obligations under the Agreement and, in order to satisfy Contractor’s requirements in this regard, Guarantors have agreed to execute this Guarantee; and

WHEREAS, Guarantors are investors, affiliates or parent companies of Operator and by virtue of their respective interests in and relationships with Operator, deem it to be in Guarantors’ best interest, based on sound business judgment, in that valuable benefits will be derived by Guarantors by virtue of the Agreement, to execute and deliver this Guarantee to the Contractor.

NOW, THEREFORE, in order to induce the Contractor to enter into the Agreement, and to satisfy such condition, and further, in order for Guarantors to

obtain the benefits resulting from the Contractor’s performance pursuant to the Agreement, Guarantors desire to enter into this Guarantee and hereby agrees to the following:

1.                    Guarantee. (a) Each Guarantor hereby severally, unconditionally, absolutely and irrevocably guarantees to Contractor the performance of all payment obligations of Operator under the Agreement (such obligations are herein collectively referred to as the “Agreement Obligations”) up to the Maximum Amount shown on Exhibit A hereto for such Guarantor. Contractor and each Guarantor hereby agree that on the date that is one (1) year after the Term Commencement Date of the Agreement, each Guarantor’s Maximum Amount shall decrease by fifty percent (50%) as shown on Exhibit A hereto for such Guarantor. The aggregate liabilities and obligations of the Guarantors hereunder shall not exceed the Agreement Obligations of the Operator under the Agreement. Notwithstanding anything to the contrary contained herein, it is agreed that Contractor shall not make a demand on any Guarantor for any amount hereunder unless Contractor has given Operator a fifteen (15) day prior written notice, a copy of which notice shall be provided to each Guarantor by sending a copy of such notice to the addresses provided in Section 6, of Contractor’s intent to demand the payment from Guarantors hereunder and has indicated to Operator in such notice the invoked breach(es) of Operator’s obligations. At the end of such fifteen (15) day period and provided that Operator has not remedied the invoked breach(es) of Operator’s obligations, Contractor shall be entitled to demand payment from Guarantors under this Guarantee.

(b)              If Contractor makes a demand for payment on Guarantors hereunder, it shall send a single notice of such demand to all Guarantors by sending a copy of such demand to the addresses provided in Section 6, which shall be copied to the Operator and which shall set forth the aggregate amount for which all of Guarantors shall be liable. Each Guarantor shall then be liable for its Guarantor Percentage (as shown on Exhibit A hereto) of such demand, not to exceed its Maximum Amount (as shown on Exhibit A hereto). Nothing in this Section 1(b) shall be construed as prohibiting Contractor from making multiple or subsequent demands or affecting the continuous guarantee(s) given hereunder; provided, however, that no Guarantor shall be liable for more than its Maximum Amount (as shown on Exhibit A hereto).

2.                    Guarantors to be Bound by Guarantee Terms. Each Guarantor acknowledges and represents that it will benefit from the Agreement and that it has received a copy of the Agreement. Each Guarantor

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hereby absolutely and unconditionally agrees to comply in all respects with and be bound by the provisions of this Guarantee.

3.                    Representations and Warranties of Guarantor. Each Guarantor severally represents and warrants to Contractor that:

(a)               Such Guarantor is duly organized, validly existing and in good standing under the laws of the jurisdiction of its incorporation or formation and has full corporate, partnership or limited liability company power to execute, deliver and perform this Guarantee.

(b)              The execution, delivery and performance of this Guarantee have been and remain duly authorized by all necessary corporate, partnership or limited liability company action and do not contravene any provision of law or of such Guarantor’s constitutional documents or contractual restriction binding on such Guarantor or its assets.

(c)               All consents, authorization and approvals of, and registrations and declarations with, any governmental authority necessary for the due execution, delivery and performance of this Guarantee by such Guarantor have been obtained and remain in full force and effect and all conditions thereof have been duly complied with, and no other action by, and no notice to or filing with, any governmental authority is required in connection with the execution, delivery or performance of this Guarantee by such Guarantor.

(d)              This Guarantee constitutes the legal, valid and binding obligation of such Guarantor enforceable against such Guarantor in accordance with its terms, subject, as to enforcement, to bankruptcy, insolvency, reorganization and other laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

4.                    Waiver. Each Guarantor hereby waives:

(a)               notice of acceptance of this Guarantee, of the creation and/or existence of any of the Agreement Obligations and of any action by Contractor in reliance hereon or in connection herewith;

(b)              presentment, demand for payment (except as expressly set forth in Section 1 above), notice of dishonor or nonpayment, protest and notice of protest with respect to the Agreement Obligations; and

(c)               except as expressly set forth in Section 1 above, any requirement that suit be brought against, or any other action by Contractor be

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taken against, or any notice of default or other notice be given to, or any demand be made on, Operator or any other person, or that any other action be taken or not taken as a condition to such Guarantor’s obligations under this Guarantee or as a condition to enforcement of this Guarantee against such Guarantor.

5.                    Amendments. No amendment of this Guarantee shall be effective unless signed by each Guarantor and Contractor. No waiver of any provision of this Guarantee nor consent to any departure by any Guarantor therefrom shall in any event be effective unless the same shall be in writing and signed by Contractor, and then such waiver or consent shall be effective only in the specific instance and for the specific purpose for which given.

6.                    Addresses for Notices. All notices and other communications provided for hereunder shall, unless otherwise specifically provided elsewhere herein, (i) be in writing and shall be addressed to the parties at their respective addresses set forth below or at such other addresses as shall be designated in a written notice to the other party, and (ii) when mailed, be effective when delivered after being deposited in the U.S. mail, registered or certified, return receipt requested, postage prepaid, and, in the case of personal delivery, when delivered at the following addresses:

if to Carlyle/Riverstone:                                                                  c/o Riverstone Holdings LLC
712 Fifth Avenue, 51st Floor
New York, NY 10019
Attention: Greg Beard
Stephen Coats

with a copy to
Fried, Frank, Harris, Shriver & Jacobson LLP
One New York Plaza
New York, NY 10004
Attention: J. Christian Nahr, Esq.

if to First Reserve:                                                                                               First Reserve Corporation
One Lafayette Place
Greenwich, CT 06830
Attention: Alan G. Schwartz

with a copy to
Gibson, Dunn & Crutcher LLP
1801 California Street, Suite 4200
Denver, CO 80202
Attention: Beau Stark, Esq.

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if to GSCP:                                                                                                                                       GS Capital Partners VI Fund, L.P.
GS Capital Partners VI Offshore Fund, L.P.
GS Capital Partners V Fund, L.P.
GS Capital Partners V Offshore Fund, L.P.
85 Broad Street
New York, NY 10004
Attention: Ken Pontarelli

with a copy to
Fried, Frank, Harris, Shriver & Jacobson LLP
One New York Plaza
New York, NY 10004
Attention: J. Christian Nahr, Esq.

if to KERN Partners:                                                                                     KERN Energy Partners I LP
KERN EnergyPartners II LP
KERN Energy Partners I U.S., LP
KERN Energy Partners II U.S., LP
200 Doll Block
116-8th Avenue
Calgary, Alberta, Canada T26 0K4
Attention: Jeff van Steenbergen

Caisse de Dépôt et Placement du Québec
Centre CDP Capital
1000, place Jean-Paul Riopelle
Montreal, Québec
CANADA H2Z 2B6
Attention: Cyrille Vittecoq

The Board of Trustees of the Leland Stanford Junior University
c/o Stanford Management Company
2770 Sand Hill Road
Menlo Park, CA 94025
Attention: Mr. Mark Hayes
Manager Real Estate & Natural Resources

with a copy to
Sidley Austin LLP
787 Seventh Avenue
New York, NY 10019

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                                                                                                                                                                                                 Attention: Anne Falvey, Esq.

and to

Ropes & Gray LLP
One International Place
Boston, MA 02110
Attention: Richard E. Gordet, Esq.

if to the Operator:                                                                                                  Cobalt International Energy, L.P.
Two Post Oak Central
1980 Post Oak Boulevard, Suite 1200
Houston, TX 77056
Attention: Doug White

if to the Contractor:                                                                                        ENSCO Offshore Company
500 North Akard Street, Suite 4300
Dallas, Texas ###-###-####
Attention: President

7.                    Effect of Certain Events. Each Guarantor agrees that such Guarantor’s liability hereunder will not be released, reduced or impaired by the occurrence of anyone or more of the following events:

(a)               The insolvency, bankruptcy, reorganization, release, receivership or discharge of Contractor;

(b)              The renewal, consolidation, extension, modification or amendment from time to time of the Agreement;

(c)               Except as expressly set forth in Section 1 above, the failure, delay, waiver or refusal by Contractor to exercise, in whole or part, any right or remedy held by Contractor with respect to the Agreement;

(d)              Lack of consideration or any other deficiency in the formation of the Agreement and any and all amendments and modifications thereof; or

(e)               Lack of corporate, partnership or limited liability company power or authority of such Guarantor or Operator.

8.                    Term. This Guarantee shall remain in full force and effect up and until the expiration of the Agreement (whether by termination by right under Section 13.1 of the Agreement, expiration of the “Primary Term,” as may be extended pursuant to the terms of the Agreement, or otherwise) or, if later, at such time as the Agreement Obligations have been fully satisfied, performed and discharged, this Guarantee

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and all obligations of each Guarantor hereunder shall terminate, all without delivery of any instrument or performance of any act by any party. Further, this Guarantee shall be released as to any Guarantor provided such Guarantor provides reasonable substitute credit support reasonably acceptable to Contractor in the form of a letter of credit, escrow account, cash prepayment or some combination thereof, in the amount of any remaining obligation of such Guarantor hereunder.

9.                    Successors and Assigns. Contractor may assign its rights hereunder to any person or entity to whom Contractor’s rights under the Agreement are assigned in accordance with the provisions of Section 18.1 of the Agreement. Each Guarantor may assign all or a portion of its rights and obligations hereunder (a) with the prior written consent of Contractor, which consent shall not be unreasonably withheld; or (b) to an affiliate or to an entity managed or advised by an affiliate of such Guarantor, provided no such assignment shall relieve such Guarantor of any liability or obligation hereunder except to the extent actually performed or satisfied by the assignee. Subject to the foregoing, this Guarantee shall be binding upon and inure to the benefit of the parties hereto and their respective successors, permitted assigns, and legal representatives.

10.              Governing Law. THE VALIDITY, CONSTRUCTION, INTERPRETATION AND EFFECT OF THIS GUARANTEE SHALL BE GOVERNED BY THE LAWS OF THE STATE OF NEW YORK, WITHOUT REGARD TO CONFLICTS OF LAW PRINCIPLES THEREOF. THE PARTIES HERETO HEREBY IRREVOCABLY SUBMIT TO THE PERSONAL JURISDICTION OF THE COURTS OF THE STATE OF NEW YORK LOCATED IN THE BOROUGH OF MANHATTAN, AND THE FEDERAL COURTS OF THE UNITED STATES OF AMERICA LOCATED IN THE STATE OF NEW YORK, BOROUGH OF MANHATTAN. EACH PARTY HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES ANY RIGHT SUCH PARTY MAY HAVE TO A TRIAL BY JURY IN RESPECT OF ANY LITIGATION DIRECTLY OR INDIRECTLY ARISING OUT OF, UNDER OR RELATING TO THIS GUARANTEE.

11.              Headings. The headings used herein are for purposes of convenience only and shall not be used in construing the provisions hereof.

12.              Several Obligations of Guarantors. NOTWITHSTANDING ANYTHING TO THE CONTRARY CONTAINED HEREIN, THE OBLIGATIONS OF GUARANTORS HEREUNDER SHALL BE SEVERAL AND NOT JOINT AND SEVERAL; NO GUARANTOR SHALL BE LIABLE FOR THE OBLIGATIONS OF ANOTHER GUARANTOR HEREUNDER; TO THE EXTENT THAT A

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GUARANTOR DOES NOT PERFORM ITS OBLIGATIONS SPECIFIED IN A DEMAND BY THE CONTRACTOR IN ACCORDANCE WITH THE TERMS HEREOF, IT SHALL REMAIN LIABLE FOR SUCH OBLIGATIONS AND THE CONTRACTOR SHALL NOT DEMAND PERFORMANCE OF SUCH OBLIGATIONS FROM ANY OTHER GUARANTOR.

13.              Indemnity and Subrogation. In addition to all such rights of reimbursement, contribution, indemnity and subrogation as the Guarantors may have under applicable law, the Operator agrees that if a payment shall be made by any Guarantor under this Guarantee, the Operator shall indemnify such Guarantor for the full amount of such payment and such Guarantor shall be subrogated to the rights of the person to whom such payment shall have been made to the extent of such payment.

14.              Counterparts. This Guarantee may be executed in multiple counterparts, all of which taken together shall constitute one document, and any signatory may sign any such counterpart. A counterpart transmitted by facsimile (including fax) shall be deemed to be an original.

[SIGNATURE PAGES FOLLOW]

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IN WITNESS WHEREOF, each Guarantor has caused this Guarantee to be duly executed and delivered effective as of this 5 day of May, 2008.

[SIGNATURE PAGE TO COBALT/ENESCO GUARANTEE]

IN WITNESS WHEREOF, each Guarantor has caused this Guarantee to be duly executed and delivered effective as of this 5 day of May, 2008.

.

[SIGNATURE PAGE TO COBALT/ENESCO GUARANTEE]

IN WITNESS WHEREOF, each Guarantor has caused this Guarantee to be duly executed and delivered effective as of this 5 day of May, 2008.

[SIGNATURE PAGE TO COBALT/ENESCO GUARANTEE]

IN WITNESS WHEREOF, each Guarantor has caused this Guarantee to be duly executed and delivered effective as of this 5 day of May, 2008.

[SIGNATURE PAGE TO COBALT/ENESCO GUARANTEE]

IN WITNESS WHEREOF, each Guarantor has caused this Guarantee to be duly executed and delivered effective as of this 5 day of May, 2008.

[SIGNATURE PAGE TO COBALT/ENESCO GUARANTEE]

IN WITNESS WHEREOF, each Guarantor has caused this Guarantee to be duly executed and delivered effective as of this 5 day of May, 2008.

[SIGNATURE PAGE TO COBALT/ENESCO GUARANTEE]

Agreed to and accepted this 5th day of May, 2008.

[SIGNATURE PAGE TO COBALT/ENESCO GUARANTEE]

EXHIBIT A

EXHIBIT A (CONTINUED)

ONE YEAR AFTER TERM COMMENCEMENT DATE OF THE AGREEMENT, THE FOLLOWING TABLE SHALL APPLY: