ARCH CAPITAL GROUP LTD. Second Amendment to RestrictedShare Unit Agreement

Exhibit 10.1

ARCH CAPITAL GROUP LTD.

Second Amendment to Restricted Share Unit Agreement

THIS AGREEMENT (the “Amendment”), dated July 9, 2009 between Arch Capital Group Ltd. (the “Company”), a Bermuda company, and Constantine Iordanou (the “Employee”).

WHEREAS, the Company granted 17,668 Restricted Share Units (the “Award”) to the Employee under the Company’s 2002 Long Term Incentive and Share Award Plan (the “Plan”) pursuant to a restricted share unit agreement, between the Company and the Employee, dated as of February 20, 2003 (the “Agreement”);

WHEREAS, the Award was amended on December 9, 2008 in order to bring it into compliance with Section 409A of the Code;

WHEREAS, the Company and the Employee wish to further amend the Award solely to conform the date of distribution of Shares under the Award to the date the fair market value of the Shares may be required to be included in income under Section 457A of the Code and Section 801(d)(2) of P.L. 110-343, Division C (the transition rules applicable to Section 457A);

WHEREAS, capitalized terms used without definition herein will have the meanings given to them in the Agreement and the Plan;

NOW, THEREFORE, in consideration of the premises and mutual covenants contained herein, the parties have agreed to amend the Agreement as follows:

1.                                       Section 2(c) of the Award is amended as to all of the Restricted Share Units subject to the Award to read in its entirety as follows:

“(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; provided, however, that, notwithstanding any provision of this Award to the contrary (including Section 11 hereof), solely to conform the date of distribution of Shares under this Award to the date the fair market value of the Shares may be required to be included in income under Section 457A of the Code and Section 801(d)(2) of P.L. 110-343, Division C, such distribution of Shares shall in no event be made later than December 31, 2017.”

2.                                       All other provisions of the Agreement, as amended, shall remain in full force and effect.  This Amendment shall be governed by and construed in accordance with the

laws of New York, without giving effect to principles of conflict of laws, and may be executed in two counterparts, each of which shall constitute one and the same instrument.

IN WITNESS WHEREOF, the undersigned have executed this Amendment on July 9, 2009.

2