Restricted Stock Unit Award Terms

Exhibit 10.4

For Awards made after August 16, 2006

Restricted Stock Unit Award Terms

under the

ACE Limited 2004 Long-Term Incentive Plan

The Participant has been granted a Restricted Stock Unit Award by ACE Limited (the “Company”) under the ACE Limited 2004 Long-Term Incentive Plan (the “Plan”). The Restricted Stock Unit Award shall be subject to the following Restricted Stock Unit Award Terms:

1. Terms of Award. Subject to the following Restricted Stock Unit Award Terms, the Participant has been granted the right to receive shares of Stock of the Company (“Units”) as of the Delivery Date. Each “Unit” represents the right to receive one share of Stock. The following words and phrases used in these Restricted Stock Unit Award Terms shall have the meanings set forth in this paragraph 1:

(a) The “Participant” is the individual recipient of the Unit Award on the specified Grant Date.

(b) The “Grant Date” is [Insert the date].

(c) The number of “Units” shall be that number of Units awarded to the Participant on the Grant Date as reflected in the corporate records and shown in the Record-Keeping System in the Participant’s individual account records.

(d) The “Delivery Date” shall be end of the Restricted Period, with respect to the applicable Units.

(e) Other words and phrases used in these Restricted Stock Unit Award Terms are defined pursuant to paragraph 9 or elsewhere in these Restricted Stock Unit Award Terms.

2. Restricted Period. Subject to the limitations of these Restricted Stock Unit Award Terms, the “Restricted Period” for each Installment of Units shall begin on the Grant Date and end as described in the following schedule (but only if the Date of Termination has not occurred before the end of the Restricted Period):

The Restricted Period shall end prior to the date specified in the foregoing schedule to the extent set forth below:

(a) For Installments as to which the Restricted Period has not ended prior to the Date of Termination, the Restricted Period for such Installments shall end upon the Participant’s Date of Termination, if the Date of Termination occurs by reason of the Participant’s death.

(b) For Installments as to which the Restricted Period has not ended prior to the Date of Termination, the Restricted Period for such Installments shall end upon the Participant’s Date of Termination, if the Date of Termination occurs by reason of the Participant’s Long-Term Disability.

(c) For Installments as to which the Restricted Period has not ended prior to the date of a Change in Control, the Restricted Period for such Installments shall end upon a Change in Control, provided that such Change in Control occurs on or before the Date of Termination.

3. Transfer and Forfeiture of Shares. Except as otherwise determined by the Committee in its sole discretion, the Participant shall forfeit the Units as of the Participant’s Date of Termination, if such Date of Termination occurs prior to the end of the Restricted Period which applies to those Installments. If the Participant’s Date of Termination has not occurred prior to the last day of the Restricted Period with respect to any Installment of the Units, then, as soon as administratively practicable following the end of such Restricted Period, that Installment of Units shall be delivered to the Participant in the form of Stock free of all restrictions.

4. Withholding. All deliveries and distributions under these Restricted Stock Unit Award Terms are subject to withholding of all applicable taxes. At the election of the Participant, and subject to such rules and limitations as may be established by the Committee from time to time, such withholding obligations may be satisfied through the surrender of shares of Stock which the Participant already owns, or to which the Participant is otherwise entitled under the Plan.

5. Transferability. Except as otherwise provided by the Committee, the Restricted Stock Unit Award may not be sold, assigned, transferred, pledged or otherwise encumbered during the Restricted Period.

6. Dividends. The Participant shall be permitted to receive cash payments equal to the dividends and distributions paid on shares of Stock to the same extent as if each Unit was a Share of Stock, and those shares were not subject to the restrictions imposed by this Agreement and the Plan; provided, however, that no dividends or distributions shall be payable to or for the benefit of the Participant with respect to record dates for such dividends or distributions occurring on or after the date, if any, on which the Participant has forfeited the Units.

7. Voting. The Participant shall not be a shareholder of record with respect to the Units and shall have no voting rights with respect to the Units during the Restricted Period.

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8. Participant’s Rights to Shares. Prior to the delivery of shares of Stock which are to be delivered pursuant to this Agreement,(a) the Participant shall not be treated as owner of the shares, shall not have any rights as a shareholder as to those shares, and shall have only a contractual right to receive them, unsecured by any assets of the Company or its subsidiaries; and (b) the Participant’s right to receive such shares will be subject to the adjustment provisions relating to mergers, reorganizations, and similar events set forth in the Plan.

9. Definitions. For purposes of these Restricted Stock Unit Award Terms, words and phrases shall be defined as follows:

(a) Change in Control. The term “Change in Control” shall be defined as set forth in the Plan.

(b) Date of Termination. A Participant’s “Date of Termination” means, with respect to an employee, the date on which the Participant’s employment with the Company and Related Companies terminates for any reason, and with respect to a Director, the date immediately following the last day on which the Participant serves as a Director; provided that a Date of Termination shall not be deemed to occur by reason of a Participant’s transfer of employment between the Company and a Related Company or between two Related Companies; further provided that a Date of Termination shall not be deemed to occur by reason of a Participant’s cessation of service as a Director if immediately following such cessation of service the Participant becomes or continues to be employed by the Company or a Related Company, nor by reason of a Participant’s termination of employment with the Company or a Related Company if immediately following such termination of employment the Participant becomes or continues to be a Director; and further provided that a Participant’s employment shall not be considered terminated while the Participant is on a leave of absence from the Company or a Related Company approved by the Participant’s employer.

(c) Director. The term “Director” means a member of the Board, who may or may not be an employee of the Company or a Related Company.

(d) Long-Term Disability. A Participant shall be considered to have a “Long-Term Disability” if the Participant is determined to be eligible for long-term disability benefits under the long-term disability plan in which the Participant participates and which is sponsored by the Company or a Related Company; or if the Participant does not participate in a long-term disability plan sponsored by the Company or a Related Company, then the Participant shall be considered to have a “Long-Term Disability” if the Committee determines, under standards comparable to those of the Company’s long-term disability plan, that the Participant would be eligible for long-term disability benefits if he or she participated in such plan.

(e) Record-Keeping System. The term “Record-Keeping System” means the record-keeping system developed and maintained by third parties contracted by the Company to keep records and facilitate Participant interfaces with respect to the Plan and awards granted thereunder.

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10. Plan Definitions. Except where the context clearly implies or indicates the contrary, a word, term, or phrase used in the Plan is similarly used in these Restricted Stock Unit Award Terms.

11. Heirs and Successors. The Restricted Stock Unit Award Terms shall be binding upon, and inure to the benefit of, the Company and its successors and assigns, and upon any person acquiring, whether by merger, consolidation, purchase of assets or otherwise, all or substantially all of the Company’s assets and business. If any benefits deliverable to the Participant under these Restricted Stock Unit Award Terms have not been delivered at the time of the Participant’s death, such benefits shall be delivered to the Designated Beneficiary, in accordance with the provisions of these Restricted Stock Unit Award Terms and the Plan. The “Designated Beneficiary” shall be the beneficiary or beneficiaries designated by the Participant in a writing filed with the Committee in such form and at such time as the Committee shall require. If a deceased Participant fails to designate a beneficiary, or if the Designated Beneficiary does not survive the Participant, any rights that would have been exercisable by the Participant and any benefits distributable to the Participant shall be distributed to the legal representative of the estate of the Participant. If a deceased Participant designates a beneficiary and the Designated Beneficiary survives the Participant but dies before the complete distribution of benefits to the Designated Beneficiary under these Restricted Stock Unit Award Terms, then any benefits distributable to the Designated Beneficiary shall be distributed to the legal representative of the estate of the Designated Beneficiary.

12. Administration. The authority to manage and control the operation and administration of these Restricted Stock Unit Award Terms shall be vested in the Committee, and the Committee shall have all powers with respect to these Restricted Stock Unit Award Terms as it has with respect to the Plan. Any interpretation of these Restricted Stock Unit Award Terms by the Committee and any decision made by it with respect to these Restricted Stock Unit Award Terms are final and binding on all persons.

13. Plan and Corporate Records Govern. Notwithstanding anything in these Restricted Stock Unit Award Terms to the contrary, these Restricted Stock Unit Award Terms shall be subject to the terms of the Plan, a copy of which may be obtained by the Participant from the office of the Secretary of the Company; and these Restricted Stock Unit Award Terms are subject to all interpretations, amendments, rules and regulations promulgated by the Committee from time to time pursuant to the Plan. Notwithstanding anything in the Restricted Stock Unit Terms to the contrary, in the event of any discrepancies between the corporate records regarding this award and the Record-Keeping System, the corporate records shall control.

14. Not An Employment Contract. The Restricted Stock Unit Award will not confer on the Participant any right with respect to continuance of employment or other service with the Company or any Related Company, nor will it interfere in any way with any right the Company or any Related Company would otherwise have to terminate or modify the terms of such Participant’s employment or other service at any time.

15. Notices. Any written notices provided for in these Restricted Stock Unit Award Terms or the Plan shall be in writing and shall be deemed sufficiently given if either hand delivered or if sent by fax or overnight courier, or by postage paid first class mail. Notices sent

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by mail shall be deemed received three business days after mailing but in no event later than the date of actual receipt. Notices shall be directed, if to the Participant, at the Participant’s address indicated by the Company’s records, or if to the Company, at the Company’s principal executive office.

16. Fractional Shares. In lieu of issuing a fraction of a share, resulting from an adjustment of the Restricted Stock Unit Award pursuant to paragraph 5.2(f) of the Plan or otherwise, the Company will be entitled to pay to the Participant an amount equal to the fair market value of such fractional share.

17. Amendment. The Restricted Stock Unit Award Terms may be amended in accordance with the provisions of the Plan, and may otherwise be amended by written agreement of the Participant and the Company without the consent of any other person.

IN WITNESS WHEREOF, the Company has caused these presents to be executed in its name and on its behalf, all as of the Grant Date.

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