UNITED STATES
SECURITIES AND EXCHANGE
COMMISSION

Washington, D.C. 20549

o

Rule 13d-1(b)

x

Rule 13d-1(c)

o

Rule 13d-1(d)

CUSIP No. G0450A105

1.

Names of Reporting Persons
Cascade Investment, L.L.C.

2.

Check the Appropriate Box if a Member of a Group (See Instructions)

(a)

o

(b)

o

3.

SEC Use Only

4.

Citizenship or Place of Organization
State of Washington

Number of
Shares
Beneficially
Owned by
Each
Reporting
Person With

5.

Sole Voting Power
 3,558,747(1)

6.

Shared Voting Power
0

7.

Sole Dispositive Power
3,558,747 (1)

8.

Shared Dispositive Power
0

9.

Aggregate Amount Beneficially Owned by Each Reporting Person
3,558,747 (1)

10.

Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions)  o

11.

Percent of Class Represented by Amount in Row (9)
6%

12.

Type of Reporting Person (See Instructions)
OO

CUSIP No. G0450A105

1.

Names of Reporting Persons
William H. Gates III

2.

Check the Appropriate Box if a Member of a Group (See Instructions)

(a)

o

(b)

o

3.

SEC Use Only

4.

Citizenship or Place of Organization
United States of America

Number of
Shares
Beneficially
Owned by
Each
Reporting
Person With

5.

Sole Voting Power
3,558,747 (1)

6.

Shared Voting Power
0

7.

Sole Dispositive Power
3,558,747 (1)

8.

Shared Dispositive Power
0

9.

Aggregate Amount Beneficially Owned by Each Reporting Person
3,558,747 (1)

10.

Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions)  o

11.

Percent of Class Represented by Amount in Row (9)
6%

12.

Type of Reporting Person (See Instructions)
IN

Item 1.

(a)

Name of Issuer
Arch Capital Group Ltd. (the “Issuer”)

(b)

Address of Issuer’s Principal Executive Offices
Wessex House, 45 Reid Street, Hamilton HM 12, Bermuda

Item 2.

(a)

Name of Person Filing
Cascade Investment, L.L.C. (“Cascade”)

William H. Gates III

(b)

Address of Principal Business Office or, if none, Residence

Cascade - 2365  Carillon Point, Kirkland, Washington 98033
Mr. Gates - One Microsoft Way, Redmond, Washington 98052

(c)

Citizenship
Cascade is a limited liability company organized under the laws of the State of Washington.

Mr. Gates is a citizen of the United States of America.

(d)

Title of Class of Securities
Common Shares, $0.01 par value per share

(e)

CUSIP Number
G0450A105

Item 3.

If this statement is filed pursuant to §§240.13d-1(b) or 240.13d-2(b) or (c), check whether the person filing is a:

Not Applicable.

 Item 4.

Ownership

Provide the following information regarding the aggregate number and percentage of the class of securities of the issuer identified in Item 1.

(a)

Amount beneficially owned:

See the responses to Item 9 on the attached cover pages.

(b)

Percent of class:

See the responses to Item 11 on the attached cover pages.

(c)

Number of shares as to which the person has:

(i)

Sole power to vote or to direct the vote

See the responses to Item 5 on the attached cover pages.

(ii)

Shared power to vote or to direct the vote

See the responses to Item 6 on the attached cover pages.

(iii)

Sole power to dispose or to direct the disposition of

See the responses to Item 7 on the attached cover pages.

(iv)

Shared power to dispose or to direct the disposition of

See the responses to Item 8 on the attached cover pages.

Item 5.

Ownership of Five Percent or Less of a Class

If this statement is being filed to report the fact that as of the date hereof the reporting person has ceased to be the beneficial owner of more than five percent of the class of securities, check the following   o.

Item 6.

Ownership of More than Five Percent on Behalf of Another Person

Not Applicable

Item 7.

Identification and Classification of the Subsidiary Which Acquired the Security Being Reported on By the Parent Holding Company or Control Person

Not Applicable

Item 8.

Identification and Classification of Members of the Group

Not Applicable

Item 9.

Notice of Dissolution of Group

Not Applicable

Item 10.

Certification

By signing below I certify that, to the best of my knowledge and belief, the securities referred to above were not acquired and are not held for the purpose of or with the effect of changing or influencing the control of the issuer of the securities and were not acquired and are not held in connection with or as a participant in any transaction having that purpose or effect.

Date: December 24, 2009

CASCADE INVESTMENT, L.L.C.

By:

*

Name: Alan Heuberger, Attorney-in-fact

for Michael Larson, Business Manager(1)

WILLIAM H. GATES III

By:

*

Name: Alan Heuberger, Attorney-in-fact(2)

CASCADE INVESTMENT, L.L.C.

By:

*

Name: Alan Heuberger, Attorney-in-fact

for Michael Larson, Business Manager(1)

WILLIAM H. GATES III

By:

*

Name: Alan Heuberger, Attorney-in-fact(2)

* By: /s/Alan Heuberger

 Alan Heuberger