SECOND OFFERING CIRCULAR SUPPLEMENT

Arch Coal, Inc.

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) to Common Stock

CUSIP No. 039380 20 9

ISIN No. US0393802097

     This second offering circular supplement relates to the offer by Arch Coal, Inc., a Delaware corporation (the “Company”), to pay a premium to holders of any and all of its 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 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 Company’s offering circular, dated November 30, 2005 (the “Offering Circular”), the offering circular supplement, dated December 5, 2005 (the “First Offering Circular Supplement”), and the accompanying letter of transmittal. This second offering circular supplement further updates the Offering Circular and the First Offering Circular Supplement and should be read in conjunction with the Offering Circular and the First Offering Circular Supplement.

     Holders of Preferred Stock who wish to request an estimate of the number of shares of Common Stock that would constitute the premium paid in the conversion offer, per share of Preferred Stock validly tendered and accepted for conversion, assuming that the conversion offer expired at midnight on the date prior to the date of inquiry, may request such information from American Stock Transfer & Trust Company, the information agent with respect to the conversion offer, toll-free at (877) 248-6417.

     As described under the caption “The Conversion Offer — Terms of the Conversion Offer” in the Offering Circular, we expressly reserve the right, in our sole discretion, to delay acceptance of shares of Preferred Stock tendered pursuant to the conversion offer or the payment of the premium. We have determined that we will not terminate the conversion offer for any reason other than a failure of a condition, and any decision to terminate the conversion offer will be made at or prior to the expiration of the conversion offer.

     With respect to the information set forth under the caption “The Conversion Offer — Acceptance; Conversion of Shares of Preferred Stock” in the Offering Circular, in all cases, issuances of shares of Common Stock for shares of Preferred Stock accepted for conversion by us pursuant to the conversion offer will be made promptly, rather than as promptly as practicable as stated therein, after the expiration date of the conversion offer.

     With respect to the information set forth under the caption “The Conversion Offer — Subsequent Repurchases of Shares of Preferred Stock” in the Offering Circular, we expressly acknowledge that we will comply with Rule 13e-4(f)(6) under the Securities Exchange Act of 1934, as amended, if we acquire any shares of Preferred Stock, other than pursuant to the conversion offer, through open market purchases, privately negotiated transactions, tender offers, conversion offers or otherwise.

     Enclosed is a new letter of transmittal for your Preferred Stock. If you have not already returned a completed letter of transmittal with respect to your Preferred Stock, please complete the enclosed letter of transmittal. If you have already returned a completed letter of transmittal, you do not need to return the enclosed letter of transmittal unless you wish to change the information set forth in the letter of transmittal that you have already returned. This new letter of transmittal, when received, will supersede your earlier letter of transmittal. In any event, you may validly withdraw shares of Preferred Stock that you have already tendered or that you may tender at any time prior to the expiration date of the conversion offer. In addition, if not previously returned, you may withdraw any shares of Preferred Stock that you tender that are not accepted by us for conversion before January 30, 2006, which is 40 business days from the commencement of the conversion offer. For a withdrawal of shares of Preferred Stock to be effective, you must comply with the appropriate procedures of DTC’s ATOP system prior to the expiration date or, if not accepted by us before January 30, 2006, the 40th business day after the commencement of the conversion offer. Any notice of withdrawal must identify the shares of Preferred Stock to be withdrawn, including the name and number of the account at DTC to be credited and otherwise comply with the procedures of DTC.

     If you have questions regarding the procedures for tendering in the conversion offer or require assistance in tendering your shares of Preferred Stock, please contact American Stock Transfer & Trust Company, the information agent for the conversion offer, toll-free at (877) 248-6417 or (718) 921-8317. You may also contact the information agent toll-free at (877) 248-6417 to receive an estimate of the number of shares of Common Stock that would constitute the premium paid in the conversion offer per share of Preferred Stock validly tendered and accepted for conversion, assuming that the conversion offer expired at midnight on the date prior to the date of inquiry. If you would like additional copies of this offering circular supplement, the Offering Circular or any supplement thereto, our annual, quarterly and current reports, proxy statement and other information that we incorporate by reference in the Offering Circular, please contact either the information agent at either telephone number set forth above or Investor Relations at Arch Coal at (314) 994-2700. Holders of Preferred Stock may also contact their brokers, dealers, commercial banks, trust companies or other nominees through which they hold their Preferred Stock with questions and requests for assistance.

The date of this offering circular supplement is December 13, 2005.