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 * Stobart John B   2. Issuer Name and Ticker or Trading Symbol Transocean Ltd. [RIG] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director _____ 10% Owner __X__ Officer (give title below) _____ Other (specify below) EVP & COO (Last) (First) (Middle) 10 CHEMIN DE BLANDONNET 3. Date of Earliest Transaction (Month/Day/Year) 03/01/2016 (Street) VERNIER, V8 1214 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 03/01/2016   M   4,794 A $ 0 (1) 22,992 D   Registered Shares 03/01/2016   M   1,254 A $ 0 (2) 24,246 D   Registered Shares 03/01/2016   M   8,303 A $ 0 (3) 32,549 D   Registered Shares 03/01/2016   M   2,740 A $ 0 (4) 35,289 D   Registered Shares 03/01/2016   M   15,612 A $ 0 (5) 50,901 D   Registered Shares 03/01/2016   F   13,635 (6) D $ 8.81 37,266 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

03/01/2016

M

4,794

03/01/2016(1)

(1)

Registered Shares

4,794

$ 0

0

D

Restricted Units

$ 0

03/01/2016

M

1,254

03/01/2016(2)

(2)

Registered Shares

1,254

$ 0

1,255

D

Restricted Units

$ 0

03/01/2016

M

8,303

03/01/2016(3)

(3)

Registered Shares

8,303

$ 0

8,304

D

Restricted Units

$ 0

03/01/2016

M

2,704

03/01/2016(4)

(4)

Registered Shares

2,704

$ 0

5,481

D

Restricted Units

$ 0

03/01/2016

M

15,612

03/01/2016(5)

(5)

Registered Shares

15,612

$ 0

31,224

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
Stobart John B 10 CHEMIN DE BLANDONNET VERNIER, V8 1214			EVP & COO

Signatures

/s/ Daniel Ro-Trock By Power of Attorney		03/03/2016
**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 equivalents, acquired on February 14, 2013, pursuant to the Issuer's long-term incentive plan. One third of such restricted units vested on March 1, 2016, resulting in delivery of registered shares to the reporting person.
(2)	Restricted Units, which are 1-for-1 equivalents, acquired on February 13, 2014, pursuant to the Issuer's long-term incentive plan. One third of such restricted units vested on March 1, 2016, resulting in delivery of registered shares to the reporting person.
(3)	Restricted Units, which are 1-for-1 equivalents, acquired on February 13, 2014, pursuant to the Issuer's long-term incentive plan. One third of such restricted units vested on March 1, 2016, resulting in delivery of registered shares to the reporting person.
(4)	Restricted Units, which are1-for-1 equivalents, acquired on February 13, 2015, pursuant to the Issuer's long-term incentive plan. One third of such restricted units vested on March 1, 2016, resulting in delivery of registered shares to the reporting person.
(5)	Restricted Units, which are 1-for-1 equivalents, acquired on February 13, 2015, pursuant to the Issuer's long-term incentive plan. One third of such restricted units vested on March 1, 2016, resulting in deliveryof registered shares to the reporting person.
(6)	Shares sold upon vesting to satisify tax witholding obligations.

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