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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1. Name and Address of Reporting Person * THIGPEN JEREMY D   2. Issuer Name and Ticker or Trading Symbol Transocean Ltd. [RIG] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director _____ 10% Owner __X__ Officer (give title below) _____ Other (specify below) President & CEO (Last) (First) (Middle) 4 GREENWAY PLAZA 3. Date of Earliest Transaction (Month/Day/Year) 03/01/2019 (Street) HOUSTON, TX 77046 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 Registered Shares 03/01/2019   M   45,716 (1) A $ 0 642,117 D   Registered Shares 03/01/2019   M   37,632 (2) A $ 0 679,749 D   Registered Shares 03/01/2019   M   54,466 (3) A $ 0 734,215 D   Registered Shares 03/01/2019   F   54,232 (4) D $ 0 679,983 D

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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

Restricted Units

$ 0

03/01/2019

M

37,633

03/01/2019

(2)

Registered Shares

37,633

$ 0

37,633

D

Restricted Units

$ 0

03/01/2019

M

54,466

03/01/2019

(3)

Registered Shares

54,466

$ 0

108,933

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
THIGPEN JEREMY D 4 GREENWAY PLAZA HOUSTON, TX 77046	X		President & CEO

Signatures

/s/ Daniel Ro-Trock By Power of Attorney		03/05/2019
**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)	Restricted Units, which are 1-for-1 share equivalents, acquired on February 11, 2016, pursuant to the Issuer's long-term incentive plan. One third of such restricted units vested on March 1, 2019, resulting in the right of the reporting person to receive the registered shares.
(2)	Restricted Units, which are 1-for-1 share equivalents, acquired on February 10, 2017, pursuant to the Issuer's long-term incentive plan. One third of such restricted units vested on March 1, 2019, resulting in the right of the reporting person to receive the registered shares. The remaining restricted share units vest as follows: 37,633 on March 1, 2020.
(3)	Restricted Units, which are 1-for-1 share equivalents, acquired on February 8, 2018, pursuant to the Issuer's long-term incentive plan. One third of such restricted units vested on March 1, 2019, resulting in the right of the reporting person to receive the registered shares. The remaining restricted share units vest as follows: 54,466 on March 1, 2020 and 54,467 on March 1, 2021.
(4)	Shares withheld upon vesting to satisfy tax withholding obligations.

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