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
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                      	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(f) of the Investment Company Act of 1940	                      	

1. Name and Address of Reporting Person *

STUART GARY M	2. Issuer Name and Ticker or Trading Symbol

ACE LTD [ ACE ]	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)

301 POST ROAD EAST, UNIT 16	3. Date of Earliest Transaction (MM/DD/YYYY)

5/17/2007		
(Street)

WESTPORT, CT 06880
(City)        (State)        (Zip)	4. If Amendment, Date Original Filed (MM/DD/YYYY)

 	6. Individual or Joint/Group Filing (Check Applicable Line)

_ X _ Form filed by One Reporting Person
___ Form filed by More than One Reporting Person	

Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned	
1.Title of Security
(Instr. 3)	2. Trans. Date	2A. Deemed Execution Date, if any	3. Trans. 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				
Ordinary Shares  	5/17/2007  	 	A (1)	  	1953.76  	A	  (1)	23507.624   (2)	D  	 	

Table II - Derivative Securities Beneficially Owned ( e.g. , puts, calls, warrants, options, convertible securities)	
1. Title of Derivate Security
(Instr. 3)	2. Conversion or Exercise Price of Derivative Security	3. Trans. Date	3A. Deemed Execution Date, if any	4. Trans. 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	7. Title and Amount of Securities Underlying Derivative Security
(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					

Explanation of Responses:	
(  1) 	Stock units, representing the right to receive Ordinary Shares, granted as director fees under the ACE Limited 2004 Long-Term Incentive Plan (the "Plan"), which meets the requirements of Rule 16b-3. Such stock units will be fully vested as of the date of the next annual ACE Limited shareholder meeting, assuming the reporting person is a director of ACE Limited on such date. Ordinary Shares will be issued for such stock units six months after the Director's termination from the Board or pursuant to such later deferral schedule as the director may elect.	
(  2) 	Total includes 334.17 share units credited at various times between July 2006 and April 2007 to the reporting person's deferred stock account pursuant to the dividend reinvestment provisions of the Plan which meets the requirements of Rule 16b-3.	

Reporting Owners	
Reporting Owner Name / Address	Relationships	
	Director	10% Owner	Officer	Other	
STUART GARY M
301 POST ROAD EAST, UNIT 16
WESTPORT, CT 06880	X				

Signatures		
By: Paul Medini, Attorney-in-fact		5/21/2007	
** Signature of Reporting Person		Date

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.	
*	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).	
Note:	File three copies of this Form, one of which must be manually signed. If space is insufficient, see Instruction 6 for procedure.	
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ACE LIMITED
Power of Attorney
Section 16(a) Reports
      The undersigned, in his or her capacity as a director and/or executive officer of ACE Limited, does hereby appoint each of Norie Bregman, Paula Cox , Robert Cusumano, Paul Medini and Lori Samson, his or her true and lawful attorney, to execute in his or her name, place and stead, in his or her capacity as a director and/or executive officer of said company, any and all reports required by Section 16(a) of the Securities Exchange Act of 1934 and the rules thereunder, and any and all amendments thereto, and all other documents necessary or incidental in connection therewith, and to file or cause to be filed the same with the Securities and Exchange Commission, the New York Stock Exchange and such other exchanges and authorities as may be necessary or appropriate.  Said attorneys shall each have full power and authority to do and perform, in the name and on behalf of the undersigned, in any and all capacities, each and every act requisite or necessary to be done in the premises, as fully and to all intents and purposes as the undersigned might or could do in person, the undersigned hereby ratifying and approving the acts of any of said attorneys.
      This Power of Attorney shall remain in full force and effect until the undersigned is no longer required to file reports under Section 16(a) of the Exchange Act with respect to the undersigned's holdings of and transactions in securities issued by ACE Limited unless earlier revoked by the undersigned in a signed writing delivered to the foregoing attorneys-in-fact.
      IN TESTIMONY WHEREOF, the undersigned has executed this instrument as of the 16th day of May, 2007.

                                                /s/Gary M. Stuart
                                                Signature
                                                Gary M. Stuart   ____________
                                                Typed or Printed Name