Exhibit 10.7

ARCH CAPITAL GROUP LTD.

Restricted Share Unit Agreement

THIS AGREEMENT, dated as of September 22, 2004, between Arch Capital Group Ltd. (the “Company”), a Bermuda company, and Ralph E. Jones, III (the “Employee”).

WHEREAS, the Employee has been granted the following award as compensation for services to be rendered; and the following terms reflect the Company’s 2002 Long Term Incentive and Share Award Plan (the “Plan”);

NOW, THEREFORE, in consideration of the premises and mutual covenants contained herein, the parties hereto agree as follows.

1.                                       Award of Share Units.  Pursuant to the provisions of the Plan, the terms of which are incorporated herein by reference, the Employee is hereby awarded 6,000 Restricted Share Units (the “Award”), subject to the terms and conditions herein set forth.  Capitalized terms used herein and not defined shall have the meanings set forth in the Plan.  In the event of any conflict between this Agreement and the Plan, the Plan shall control.

2.                                       Terms and Conditions.  It is understood and agreed that the Award of Restricted Share Units evidenced hereby is subject to the following terms and conditions:

(a)                                  Vesting of Award.  Subject to Section 2(b) below and the other terms and conditions of this Agreement, this Award shall become vested in three equal annual installments, commencing on the date hereof and thereafter on the first and second anniversaries thereof.  Unless otherwise provided by the Company, all amounts receivable in connection with any adjustments to the Shares under Section 4(c) of the Plan or Section 2(e) below shall be subject to the vesting schedule in this Section 2(a).

(b)                                 Termination of Service; Forfeiture of Unvested Share Units.  In the event the Employee ceases to be an employee of the Company prior to the date the Restricted Share Units otherwise become vested (i) due to his or her death or Permanent Disability (as defined in the Company’s Incentive Compensation Plan) or (ii) due to termination (A) by the Company not for Cause (as defined in the Company’s Incentive Compensation Plan) or (B) by the Employee for Good Reason (as defined in the Employment Agreement, dated as of June 4, 2003, between the Employee and Arch Insurance Group Inc.), the Restricted Share Units shall become immediately vested in full upon such termination of employment.  In the event of termination of employment (other than by the Company for Cause) after the attainment of Retirement Age (as defined in the Company’s Incentive Compensation Plan), the Restricted

Share Units shall continue to vest on the schedule set forth in Section 2(a) above so long as the Employee does not engage in any activity in competition with any activity of the Company or any of its Subsidiaries other than serving on the board of directors (or similar governing body) of another company or as a consultant for no more than 26 weeks per calendar year (“Competitive Activity”).  In the event the Employee engages in a Competitive Activity, any unvested Restricted Share Units shall be forfeited by the Employee and become the property of the Company.  If the Employee ceases to be an Employee of the Company for any other reason prior to the date the Restricted Share Units become vested, the unvested Restricted Share Units shall be forfeited by the Employee and become the property of the Company.  For purposes of this Agreement, service with any of the Company’s Subsidiaries (as defined in the Plan) shall be considered to be service with the Company.

(c)                                  Distribution of Shares.  At the time the Employee ceases to be an Employee of the Company for any reason, the Company shall distribute to the Employee (or his or her heirs in the event of the Employee’s death) a number of Shares equal to the number of vested Restricted Share Units then held by the Employee.

(d)                                 Rights and Restrictions.  The Restricted Share Units shall not be transferable, other than pursuant to will or the laws of descent and distribution.  Prior to vesting of the Restricted Share Units and delivery of the Shares to the Employee following his termination of employment, the Employee shall not have any rights or privileges of a shareholder as to the Shares subject to the Award.  Specifically, the Employee shall not have the right to receive dividends or the right to vote such Shares prior to vesting of the Award and delivery of the Shares.

(e)                                  Adjustments for Recapitalization and Dividends.  In the event that, prior to the distribution of Shares pursuant to Section 2(c) above, any dividend in Shares, recapitalization, Share split, reverse split, reorganization, merger, consolidation, spin-off, combination, repurchase, or share exchange, or other such change affects the Shares such that they are increased or decreased or changed into or exchanged for a different number or kind of shares, other securities of the Company or of another corporation or other consideration, then in order to maintain the proportionate interest of the Employee and preserve the value of the Award, there shall automatically be substituted for each Share subject to the Award the number and kind of shares, other securities or other consideration (including cash) into which each outstanding Share shall be changed or for which each such Share shall be exchanged.

(f)                                    Dividend Equivalents.  As of each date on which a cash dividend is paid on Shares, there shall be granted to the Employee that number of additional Restricted Share Units (including fractional units) determined by (i) multiplying the amount of such dividend per Share by the number of Restricted Share Units held by the Employee, and (ii) dividing the total so determined by the Fair Market Value of a Share on the date of payment of such cash dividend.  The Restricted Share Units granted pursuant to this Section 2(f) will have the same terms and

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conditions (including vesting dates) as the Restricted Share Units with respect to which they are granted.

(g)                                 No Right to Continued Employment.  This Award shall not confer upon the Employee any right with respect to continuance of employment by the Company nor shall this Award interfere with the right of the Company to terminate the Employee’s employment at any time.

3.                                       Transfer of Shares.  The Shares delivered hereunder, or any interest therein, may be sold, assigned, pledged, hypothecated, encumbered, or transferred or disposed of in any other manner, in whole or in part, only in compliance with the terms, conditions and restrictions as set forth in the governing instruments of the Company, applicable United States federal and state securities laws or any other applicable laws or regulations and the terms and conditions hereof.

4.                                       Expenses of Issuance of Shares.  The issuance of stock certificates hereunder shall be without charge to the Employee.  The Company shall pay, and indemnify the Employee from and against any issuance, stamp or documentary taxes (other than transfer taxes) or charges imposed by any governmental body, agency or official (other than income taxes) or by reason of the issuance of Shares.

5.                                       Withholding.  The Employee shall pay to the Company or make arrangements satisfactory to the Committee regarding payment of any federal, state or local taxes of any kind required by law to be withheld with respect to the Award and the Company shall, to the extent permitted or required by law, have the right to deduct from any payment of any kind otherwise due to the Employee, federal, state and local taxes of any kind required by law to be withheld.

6.                                       References.  References herein to rights and obligations of the Employee shall apply, where appropriate, to the Employee’s legal representative or estate without regard to whether specific reference to such legal representative or estate is contained in a particular provision of this Agreement.

7.                                       Notices.  Any notice required or permitted to be given under this Agreement shall be in writing and shall be deemed to have been given when delivered personally or by courier, or sent by certified or registered mail, postage prepaid, return receipt requested, duly addressed to the party concerned at the address indicated below or to such changed address as such party may subsequently by similar process give notice of:

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If to the Company:

Arch Capital Group Ltd.
Wessex House, 4th Floor
45 Reid Street
Hamilton HM 12 Bermuda
Attn.: Secretary

If to the Employee:

To the last address delivered to the Company by the
Employee in the manner set forth herein.

8.                                       Governing Law.  This Agreement shall be governed by and construed in accordance with the laws of New York, without giving effect to principles of conflict of laws.

9.                                       Entire Agreement.  This Agreement and the Plan constitute the entire agreement among the parties relating to the subject matter hereof, and any previous agreement or understanding among the parties with respect thereto is superseded by this Agreement and the Plan.

10.                                 Counterparts.  This Agreement may be executed in two counterparts, each of which shall constitute one and the same instrument.

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IN WITNESS WHEREOF, the undersigned have executed this Agreement as of the date first above written.

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