<Page> Exhibit 5.1 MAPLES AND CALDER Cayman Europe Asia ACE Limited The ACE Building 30 Woodbourne Building Hamilton, HM 08 Bermuda 31 August, 2004 Dear Sirs ACE LIMITED We have acted as Cayman Islands legal advisers to ACE Limited (the "COMPANY") in connection with the Company's registration statement on Form S-3, including all amendments or supplements thereto (the "REGISTRATION STATEMENT"), filed with the Securities and Exchange Commission under the Securities Act of 1933, as amended, relating, to the offering and sale, INTER ALIA, of ordinary shares of the Company (the "ORDINARY SHARES"), preferred shares of the Company (the "PREFERRED SHARES"), depositary shares representing preferred shares of the Company (the "DEPOSITARY SHARES"), debt securities (the "DEBT SECURITIES"), warrants to purchase ordinary shares (the "WARRANTS TO PURCHASE ORDINARY SHARES"), warrants to purchase preferred shares (the "WARRANTS TO PURCHASE PREFERRED SHARES"), warrants to purchase debt securities (the "WARRANTS TO PURCHASE DEBT SECURITIES" and, together with the Warrants to Purchase Ordinary Shares and the Warrants to Purchase Preferred Shares, the "WARRANTS"), stock purchase contracts (the "STOCK PURCHASE CONTRACTS") and stock purchase units (the "STOCK PURCHASE UNITS") of the Company and debt securities of ACE INA Holdings Inc. ("ACE INA") guaranteed by the Company (the "ACE INA DEBT SECURITIES"), in one or more offerings up to an aggregate initial offering price of US$1,500,000,000. We are furnishing this opinion as Exhibit 5.1 to the Registration Statement. 1 DOCUMENTS REVIEWED For the purposes of this opinion, we have reviewed only originals, copies or final drafts of the following documents: 1.1 the certificate of incorporation of the Company and the Memorandum and Articles of Association of the Company as adopted on 14 January, 1993 and amended on February, 1998 and 22 January, 2002; 1.2 a Certificate of the Assistant Secretary of the Company (the "SECRETARY'S CERTIFICATE") in the form attached certifying, INTER ALIA, that certain resolutions were passed by the <Page> MAPLES CALDER Cayman Europe Asia 2 Board of Directors of the Company on 27 May, 2004 ( the "RESOLUTIONS"); 1.3 the Registration Statement, including the form of the indenture pursuant to which the Company's subordinated debt securities will be issued (the "ACE SUBORDINATED DEBT INDENTURE"); 1.4 the Indenture dated as of 15 March, 2002 between the Company and J.P. Morgan Trust Company, National Association (as successor to The First National Bank of Chicago) as trustee (the "ACE SENIOR DEBT INDENTURE"); 1.5 the Indenture dated as of 1 August, 1999 between the Company, ACE INA and J.P. Morgan Trust Company, National Association (as successor to The First National Bank of Chicago) as trustee (the "ACE INA SENIOR DEBT INDENTURE"); 1.6 the Indenture dated as of 1 December, 1999 between the Company, ACE INA and J.P. Morgan Trust Company, National Association (as successor to The First National Bank of Chicago) as trustee (the "ACE INA SUBORDINATED DEBT INDENTURE"); 1.7 a Certificate of Good Standing issued by the Registrar of Companies (the "CERTIFICATE OF GOOD STANDING"); and 1.5 a Certificate of General Counsel and Secretary of the Company in the form attached. 2 ASSUMPTIONS The following opinion is given only as to, and based on, circumstances and matters of fact existing and known to us on the date of this opinion. This opinion only relates to the laws of the Cayman Islands which are in force on the date of this opinion. In giving this opinion we have relied (without further verification) upon the completeness and accuracy of the Officer's Certificate and the Certificate of Good Standing. We have also relied upon the following assumptions, which we have not independently verified: 2.1 copy documents, conformed copies or drafts of documents provided to us are true and complete copies of, or in the final forms of, the originals; 2.2 all signatures, initials and seals are genuine; 2.3 the Company will receive money or money's worth in consideration for the issue of the Ordinary Shares and the Preferred Shares, and that none of the Ordinary Shares or the Preferred Shares will be issued for less than par value; 2.4 there will be sufficient Ordinary Shares and Preferred Shares authorised for issue under the Company's memorandum of association; and <Page> MAPLES CALDER Cayman Europe Asia 3 2.5 there is nothing under any law (other than the law of the Cayman Islands) which would or might affect the opinions hereinafter appearing. 3 OPINION Based upon, and subject to, the foregoing assumptions and having regard to such legal considerations as we deem relevant, we are of the opinion that: 1. The Company is an exempted company duly incorporated and validly existing and, based on the certificate issued by the Cayman Islands Registrar of Companies, in good standing under the laws of the Cayman Islands. 2. With respect to Ordinary Shares (including the Ordinary Shares issuable upon the exercise of the Ordinary Share Warrants), when the issue of such Ordinary Shares has been recorded in the share register of the Company and the subscription price of such Ordinary Shares (being not less than the par value of the Ordinary Shares) has been fully paid in cash or other consideration approved by the Board of Directors of the Company or a duly constituted and acting committee thereof (such Board of Directors or committee being hereinafter referred to as the Board), the Ordinary Shares will be authorized and validly issued, fully paid and non-assessable. 3. With respect to Preferred Shares (including the Preferred Shares issuable upon the exercise of the Preferred Share Warrants, and the Preferred Shares to be represented by the Depositary Shares), when the Board has taken all necessary corporate action to approve and establish the terms of the Preferred Shares and related matters, the issue of such Preferred Shares has been recorded in the share register of the Company and the contractual subscription price of such Preferred Shares (being not less than the par value of the Preferred Shares) has been fully paid in cash or other consideration approved by the Board, the Preferred Shares will be authorized, validly issued, fully paid and non-assessable. 4. With respect to the Warrants and the warrant agreements pursuant to which the Warrants are to be issued (the "Warrant Agreements"), when the Board has taken all necessary corporate action to approve the terms of the Warrants and the Warrant Agreements and related matters, the issue of the Warrants and the entry by the Company into the Warrant Agreements will be authorized by the Company. 5. The entry by the Company into the ACE Senior Debt Indenture, the ACE INA Senior Debt Indenture and the ACE INA Subordinated Debt Indenture have been authorized by the Company. When executed by an Authorized Officer (as defined in the Resolutions) of the Company, the entry by the Company into the ACE Subordinated Debt Indenture will be authorized by the Company. <Page> MAPLES CALDER Cayman Europe Asia 4 6. The Senior Notes to be issued pursuant to the ACE Senior Debt Indenture have been authorized by the Company. When executed by an Authorized Officer (as defined in the Resolutions) of the Company, the Subordinated Notes will be authorized by the Company. 7. The guarantee by the Company of the ACE INA Debt Securities has been authorized. 8. The issue by the Company of mandatorily convertible securities has been authorised, and when the Board has taken all necessary corporate action to approve the terms of the Stock Purchase Contracts and the issue by the Company of the Stock Purchase Units, the entry by the Company into the Stock Purchase Contracts and the issue by the Company of the Stock Purchase Units will be authorized by the Company. Except as specifically stated herein, we make no comment with respect to any representations and warranties which may be made by or with respect to the Company in any of the documents or instruments cited in this opinion or otherwise with respect to the commercial terms of the transactions the subject of this opinion. We hereby consent to filing of this opinion as an exhibit to the Registration Statement and to the reference to our firm under the heading "Legal Matters" in the prospectus included in the Registration Statement. In the giving our consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the Rules and Regulations of the Commission thereunder. Yours faithfully, MAPLES AND CALDER - -----------------