Ownership Submission
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
OMB APPROVAL
OMB Number: 3235-0287
Expires: January 31, 2005
Estimated average burden hours per response... 0.5

(Print or Type Responses)
1. Name and Address of Reporting Person *
DAVIS HOWARD E
  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, CAO & CIO
(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 08/17/2017   J   20,000 A $ 7.32 20,000 I By IRA (1)
Registered Shares 03/01/2019   M   14,368 (2) A $ 0 79,100 D  
Registered Shares 03/01/2019   M   12,946 (3) A $ 0 92,046 D  
Restricted Shares 03/01/2019   M   16,729 (4) A $ 0 108,775 D  
Registered Shares 03/01/2019   F   10,726 (5) D $ 0 98,049 D  

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
Persons who respond to the collection of information contained in this form are not required to respond unless the form displays a currently valid OMB control number. SEC 1474 (9-02)

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   12,946   03/01/2019   (3) Registered Shares 12,946 $ 0 12,946 D  
Restricted Units $ 0 03/01/2019   M   16,729   03/01/2019   (4) Registered Shares 16,729 $ 0 33,458 D  

Reporting Owners

Reporting Owner Name / Address Relationships
 Director  10% Owner  Officer  Other
DAVIS HOWARD E
4 GREENWAY PLAZA
HOUSTON, TX 77046
      EVP, CAO & CIO  

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) As previously reported on August 17, 2017, the reporting person indirectly owns 20,000 registered shares through an Individual Retirement Account.
(2) 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.
(3) 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: 12,946 on March 1, 2020.
(4) 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: 16,729 on March 1, 2020, and 16,729 on March 1, 2021.
(5) Shares withheld upon vesting to satisfy tax withholding obligations.

Note: File three copies of this Form, one of which must be manually signed. If space is insufficient, see Instruction 6 for procedure.

Potential persons who are to respond to the collection of information contained in this form are not required to respond unless the form displays a currently valid OMB number.