Exhibit (a)(1)(G)

ARCH COAL, INC.

LETTER TO CLIENTS

Offer To Pay a Premium Upon The Conversion

of up to an Aggregate of 2,874,926 Shares of Its

5% Perpetual Cumulative Convertible Preferred Stock

(Liquidation Preference $50.00 Per Share)

CUSIP No. 039380 20 9

ISIN No. US0393802097

Pursuant to the Offering Circular dated November 30, 2005,

the Offering Circular Supplement dated December 5, 2005,

the Second Offering Circular Supplement dated December 13, 2005

and the Third Offering Circular Supplement dated December 16, 2005

THE CONVERSION OFFER WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME,

ON DECEMBER 30, 2005 (THE “EXPIRATION DATE”), UNLESS THE CONVERSION

OFFER IS EXTENDED OR EARLIER TERMINATED.

SHARES OF 5% PERPETUAL CUMULATIVE CONVERTIBLE PREFERRED STOCK (LIQUIDATION PREFERENCE $50.00 PER SHARE) (“PREFERRED STOCK”) TENDERED IN THE CONVERSION OFFER MAY BE WITHDRAWN AT ANY TIME PRIOR TO THE EXPIRATION DATE (AS IT MAY BE EXTENDED). IN ADDITION, YOU MAY WITHDRAW ANY TENDERED SHARES OF PREFERRED STOCK AFTER JANUARY 30, 2006, IF WE HAVE NOT ACCEPTED THEM FOR CONVERSION.

To Our Clients:

      We are enclosing herewith an Offering Circular, dated November 30, 2005 (the “Offering Circular”), and an Offering Circular Supplement, dated December 5, 2005, a Second Offering Circular Supplement, dated December 13, 2005 and a Third Offering Circular dated December 16, 2005 (collectively, the “Offering Circular Supplements”), of Arch Coal, Inc., a Delaware corporation (the “Company”), and a letter of transmittal (the “Letter of Transmittal”) relating to the offer by the Company to pay a premium to holders of any and all of the outstanding Preferred Stock who elect to convert their shares of Preferred Stock to the Company’s Common Stock, $.01 par value (“Common Stock”), in accordance with the terms of the Preferred Stock and upon the terms and subject to the conditions set forth in the Offering Circular, the Offering Circular Supplements and the accompanying Letter of Transmittal. The premium offered in this conversion offer is an amount of shares of the Company’s Common Stock valued at $3.50, as determined by dividing (i) $3.50 by (ii) the volume-weighted average of the reported sales prices on the New York Stock Exchange of the Company’s Common Stock during the 10 trading days ending at the close of the second trading day prior to the expiration of this conversion offer (including any extension), per share of Preferred Stock validly tendered and accepted for conversion. Holders who validly tender shares of Preferred Stock for conversion will receive the premium in addition to the number of shares of Common Stock issuable upon conversion pursuant to the conversion terms of the Preferred Stock. As of the date of the Offering Circular, the conversion ratio for the Preferred Stock was 2.3985 shares of the Company’s Common Stock for each share of Preferred Stock validly converted. On November 29, 2005, 2,874,926 shares of the Company’s Preferred Stock were outstanding. Certain terms used but not defined herein have the meanings ascribed to them in the Offering Circular.

      The Conversion Offer is subject to certain conditions. See the section of the Offering Circular entitled “The Conversion Offer — Conditions to the Conversion Offer.”

      We are the holder of your shares of Preferred Stock through our account with the Depository Trust Company (“DTC”). A tender of such shares of Preferred Stock can be made only by us as a DTC participant

and pursuant to your instructions. The enclosed Letter of Transmittal is furnished to you for your information only and cannot be used by you to tender shares of Preferred Stock held by us for your account.

      We request instructions as to whether you wish to tender any or all of the shares of Preferred Stock held by us through our DTC account pursuant to the terms and conditions set forth in the Offering Circular, the Offering Circular Supplements and the Letter of Transmittal.

      We urge you to read the Offering Circular, including the documents incorporated by reference therein, the Offering Circular Supplements and the Letter of Transmittal carefully before instructing us to tender your shares of Preferred Stock. You may use the attached form to give your instructions.

PLEASE RETURN YOUR INSTRUCTIONS TO US IN THE ENCLOSED ENVELOPE OR CONTACT YOUR REPRESENTATIVE WITH INSTRUCTIONS TO PERMIT US TO TENDER YOUR SHARES OF PREFERRED STOCK PRIOR TO THE EXPIRATION DATE.

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INSTRUCTIONS TO THE DEPOSITORY TRUST COMPANY PARTICIPANT

To the Participant of The Depository Trust Company:

     The undersigned hereby acknowledges receipt of the Offering Circular, dated November 30, 2005 (the “Offering Circular”), and the Offering Circular Supplement, dated December 5, 2005 the Second Offering Circular Supplement, dated December 13, 2005, and the Third Offering Circular Supplement, dated December 16, 2005 (collectively, the “Offering Circular Supplements”), of Arch Coal, Inc., a Delaware corporation (the “Company”), and the Letter of Transmittal, which together set forth the terms and conditions of the offer (the “Conversion Offer”) by the Company to pay a premium to holders of any and all of the Company’s outstanding 5% Perpetual Cumulative Convertible Preferred Stock (Liquidation Preference $50.00 Per Share) (“Preferred Stock”) who elect to convert their shares of Preferred Stock to shares of the Company’s Common Stock, $0.01 par value (“Common Stock”), in accordance with the terms of the Preferred Stock and upon the terms and subject to the conditions set forth in the Offering Circular, the Offering Circular Supplements and in the Letter of Transmittal. Certain terms used but not defined herein have the meanings ascribed to them in the Offering Circular.

     This will instruct you as to the action to be taken by you, for the account of the undersigned, relating to the Conversion Offer.

The number of shares of Preferred Stock held by you through your account with The Depository Trust Company (“DTC”) for the account of the undersigned is (fill in amount):   shares of Preferred Stock.

     With respect to the Conversion Offer, the undersigned hereby instructs you (check appropriate box):

o  To tender the following shares of Preferred Stock held by you for the account of the undersigned, upon the terms and subject to the conditions set forth in the Offering Circular, the Offering Circular Supplements and the Letter of Transmittal (insert number of shares of Preferred Stock to be tendered, if any):

 shares of Preferred Stock.*

The number of shares of the Company’s Common Stock that the undersigned will beneficially own immediately prior to the conversion of the tendered shares of Preferred Stock, excluding shares to be issued upon conversion of shares of Preferred stock in the Conversion Offer is (insert number of shares of Common Stock):

 shares of Common Stock.

The number of shares of the Company’s Common Stock that the undersigned will beneficially own immediately prior to the conversion of the tendered shares of Preferred Stock, excluding shares to be issued upon conversion of shares of Preferred stock in the Conversion Offer is (insert number of shares of Common Stock):

 shares of Common Stock.

The number of shares of Preferred Stock beneficially owned by the undersigned that are held by Participants other than you, which the undersigned is tendering for conversion (insert number of shares of Preferred Stock):

 shares of Preferred Stock.

o  Not to tender any shares of Preferred Stock held by you for the account of the undersigned.

     The undersigned represents that either (i) upon the conversion of the shares of Preferred Stock tendered pursuant to the Conversion Offer, the undersigned will not beneficially own in excess of 9.9% of the aggregate number of shares of the Company’s Common Stock outstanding immediately after giving effect to such conversion or (ii) these instructions set forth (a) the number of shares of Common Stock that the undersigned will beneficially own at the time of the conversion of the tendered shares of Preferred Stock, excluding shares issued upon conversion of shares of Preferred Stock in the Conversion Offer, (b) the number of shares of Preferred Stock the Participant is instructed to tender hereby, and (c) the number of shares of Preferred Stock being tendered through other Participants, and that the undersigned is requesting that the Company does not accept for conversion any shares of Preferred Stock to the extent that upon conversion of such shares of Preferred Stock the undersigned’s beneficial ownership of the Company’s Common Stock will exceed 9.9% of the aggregate number of shares of the Company’s Common Stock outstanding following the Conversion Offer.

*  Unless otherwise indicated, the entire number of shares of Preferred Stock indicated above as held by the Participant for the account of the undersigned will be tendered.

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SIGN HERE

Name(s) of beneficial owner(s):

Signature(s):

Name(s):

(Please Print)

Address(es):

Telephone Number(s):

Taxpayer Identification or

Social Security Number(s):

Date:

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