FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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(Print or Type Responses)

1. Name and Address of Reporting Person * KEMP JOHN RANDOLPH III   2. Issuer Name and Ticker or Trading Symbol Kosmos Energy Ltd. [KOS] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director _____ 10% Owner _____ Officer (give title below) _____ Other (specify below) (Last) (First) (Middle) C/O KOSMOS ENERGY, LLC, 8176 PARK LANE, SUITE 500 3. Date of Earliest Transaction (Month/Day/Year) 01/09/2012 (Street) DALLAS, TX 75231 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) _X_ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price Common Shares 01/09/2012   S   500 D $ 13.91 108,024 D   Common Shares 01/10/2012   S   14,500 D $ 13.9 93,524 D   Common Shares               1,800 I See Footnotes (1) Common Shares               662,816 I See Footnotes (2)

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
KEMP JOHN RANDOLPH III C/O KOSMOS ENERGY, LLC 8176 PARK LANE, SUITE 500 DALLAS, TX 75231	X

Signatures

/s/ William S. Hayes, attorney-in-fact		01/10/2012
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1)	These shares are owned by the reporting person's wife. The reporting person disclaims beneficial ownership of these shares except to the extent of his pecuniary interest therein.
(2)	These shares granted under the Issuer's Long Term Incentive Plan are directly owned by the Rhonda N. Kemp 2011 Trust No. 1, Rhonda N. Kemp 2011 Trust No. 2, John R. Kemp, IV 2011 Trust No. 1, John R. Kemp, IV 2011 Trust No. 2, John R. Kemp, III 2011 Grantor Retained Annuity Trust and the Rosalind I. Kemp 2011 Grantor Retained Annuity Trust in the amount of 26,579, 26,579, 26,579, 26,579, 278,250 and 278,250 common shares, respectively. The reporting person disclaims beneficial ownership of these shares except to the extent of his pecuniary interest therein.

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