PUT/CALL AGREEMENT

Exhibit 10.27

EXECUTION VERSION

PUT/CALL AGREEMENT

by and among

H-LINES HOLDING CORP.

and the

OPTIONHOLDERS

signatory hereto

Dated as of July 7, 2004.

PUT/CALL AGREEMENT

PUT/CALL AGREEMENT, dated as of July 7, 2004 (this “Agreement”), by and among H-LINES HOLDING CORP., a Delaware corporation (“H-Lines”) and each of the optionholders signatory hereto (each, an “Optionholder”). H-Lines and the Optionholders are each individually referred to herein as a “Party” and together collectively referred to herein as the “Parties”.

WHEREAS, reference is made to that certain Agreement and Plan of Merger, dated May 22, 2004, by and among H-Lines, H-Lines Subcorp., a Delaware corporation and a wholly-owned subsidiary of H-Lines, Horizon Lines Holding Corp. (“Horizon”), and TC Group, L.L.C., a Delaware limited liability company (such agreement, as amended or modified, the “Merger Agreement”);

WHEREAS, reference is made to that certain voting trust agreement, dated as of July 7, 2004, by and among Horizon and the Optionholders (such agreement, as amended or modified, the “Horizon Voting Trust Agreement”).

WHEREAS, pursuant to the Merger Agreement, as a condition to any right to elect to retain all or any portion of such Optionholder’s options to purchase shares of common stock, par value $.01, of Horizon (the “Rollover Options”) in lieu of such Optionholder’s right to receive a portion of the Merger Consideration, such Optionholder shall agree to enter into this Agreement;

WHEREAS, the Rollover Options provide for the Optionholder to purchase shares of common stock, par value $.01, of Horizon (the “Horizon Common Stock”) at the exercise price stated therein (the “Exercise Price”).

NOW, THEREFORE, the parties hereto hereby agree as follows:

1. Definitions. Capitalized terms used in this Agreement and not otherwise defined herein shall have their respective meanings set forth in the Merger Agreement.

2. Put Right; Call Right.

(a) Put Right. H-Lines hereby grants to each Optionholder, individually, the right and option (but not the obligation) to require H-Lines to exchange, at any time and from time to time, all or any portion of the shares of Horizon Common Stock issued upon exercise of the Rollover Options (such shares issued upon exercise, the “Horizon Shares”) held by such Optionholder for shares of redeemable preferred stock, par value $0.01 per share, of H-Lines (the “H-Lines Preferred Stock”) and shares of common stock, par value $0.01 per share, of H-Lines (the “H-Lines Common Stock”) (such shares of H-Lines Preferred Stock and H-Lines Common Stock together, the “H-Lines Shares”) in the ratio determined in accordance with Section 2(e) (such right of Optionholder, the “Put Right”).

(b) Call Right. Each Optionholder, on behalf of itself only, hereby grants to H-Lines the right and option (but not the obligation) to require such Optionholder to surrender, at

any time and from time to time, all or any portion of the Horizon Shares held by such Optionholder in exchange for H-Lines Shares in the ratio determined in accordance with Section 2(e) (such right and option of H-Lines, the “Call Right”).

(c) Dividend Payments. Upon exercise of the Put Right or Call Right, in addition to the H-Lines Shares to be received by the Optionholder in exchange for Horizon Shares, such Optionholder shall receive from H-Lines any dividends or distributions that would have been received by such Optionholder if such Optionholder owned the H-Lines Shares being received pursuant to the exercise of the Put Right or Call Right on the date hereof (the “Past Dividend Payments”).

(d) Notice. (i) An Optionholder may exercise its Put Right by providing written notice to H-Lines indicating the number of Horizon Shares which are to be exchanged and the effective date of such exercise; provided, that such effective date shall not be less than one business day after the date of receipt of the written notice.

(ii) H-Lines may exercise its Call Right with respect to any Optionholder by providing written notice to such Optionholder indicating the number of Horizon Shares which are to be exchanged and the effective date of such exercise; provided, that such effective date shall not be less than one business day after the date of receipt of the written notice.

(e) Exchange Ratio. Upon exercise of either the Put Right or the Call Right, the number of H-Lines Shares which the applicable Optionholder shall receive in exchange for the Horizon Shares shall be determined in the following manner. The value attributable to each share of H-Lines Common Stock and H-Lines Preferred Stock shall be $8 and $10, respectively. The ratio of shares of H-Lines Common Stock and H-Lines Preferred Stock to be received by such Optionholder shall equal 1 share of H-Lines Common Stock to 15 shares of H-Lines Preferred Stock (together, a “Unit”). The value attributable to each Horizon Share (the “Horizon Common Stock Value”) being exchanged shall equal the Cash Per Fully Diluted Share (as defined in the Merger Agreement). Each Horizon Share shall be exchangeable into a number of Units equal to the Horizon Common Stock Value divided by $158.

(f) Reservation of Shares and Agreement to be Bound. H-Lines shall at all times keep reserved such number of H-Lines Common Stock H-Lines Preferred Stock into which all the Horizon Shares held by the Optionholders at such time could be exchanged if all the Roll-Over Options were exercised and the Put Rights or the Call Rights are exercised in full.

(e) Closing. (i) The closing of the redemption and exchange of Horizon Shares for H-Lines Shares pursuant to exercise of the Put Right or Call Right as set forth in this Section (the “Closing”) shall take place at the offices of Schulte Roth & Zabel LLP, 919 Third Avenue, New York, New York 10022, on the Business Day (the “Closing Date”) set forth in the written notice.

(ii) At the Closing, (A) H-Lines shall issue and deliver to the applicable Optionholder, certificates representing the Units to be issued by it pursuant to this Agreement and cash representing the Past Dividend Payments (without any interest therefor), (B) the applicable Optionholder shall deliver to H-Lines certificates representing the Horizon Shares

2

to be exchanged therefor, (C) such Optionholder shall deliver duly executed copies of each of the Stockholders Agreement and the Voting Trust Agreement, dated July 7 2004, by and among H-Lines and the stockholders listed on the signature pages thereto (as amended or modified, the “H-Lines Voting Trust Agreement” and together with the Horizon Voting Trust Agreement, the “Voting Trust Agreements”), and (D) each party to this Agreement shall deliver to the other such other documents, instruments and writings as may be required to be delivered in accordance with this Agreement or as may be reasonably requested by such other party.

3. Representations and Warranties of Optionholder. Each Optionholder, on behalf of itself only, makes the following representations and warranties.

(a) Such Optionholder is, and will be, acquiring Horizon Shares and H-Lines Shares for investment for its own account and not with a view to, or for resale in connection with, the distribution or other disposition thereof in violation of the Securities Act. Such Optionholder agrees that it will not, directly or indirectly, offer, transfer, sell, pledge, hypothecate or otherwise dispose of any Horizon Shares or H-Lines Shares (or solicit any offers to buy, purchase, or otherwise acquire or take a pledge of any Horizon Shares or H-Lines Shares), except in compliance with the Securities Act, the rules and regulations promulgated thereunder, applicable state securities laws, the provisions of this Agreement, the Stockholders Agreement and the Voting Trust Agreements. Such Optionholder represents and warrants that no other person or entity will have any interest, beneficial or otherwise, in the Horizon Shares or H-Lines Shares acquired by such Optionholder except as provided under the Stockholders Agreement and the Voting Trust Agreements.

(b) Such Optionholder acknowledges that it has been advised that (i) neither the Horizon Shares nor the H-Lines Shares are registered under the Securities Act, and neither Horizon nor H-Lines has any obligation to effectuate any such registration, (ii) the Horizon Shares and H-Lines Shares must be held indefinitely and Optionholder must continue to bear the economic risk of the investment in the Horizon Shares and H-Lines Shares unless they are subsequently registered under the Securities Act or an exemption from such registration is available, (iii) Rule 144 promulgated under the Securities Act is not presently available with respect to the sale of any securities of Horizon or H-Lines, and neither Horizon nor H-Lines has no obligation nor any intention to make such Rule available, (iv) when and if any Horizon Shares or H-Lines Shares may be disposed of without registration in reliance on Rule 144, the amounts that may be disposed of may be limited in accordance with the terms and conditions of such Rule, (v) if the Rule 144 exemption is not available, public sale without registration will require compliance with Regulation D or some other exemption under the Securities Act, (vi) restrictive legends will be placed on the certificates representing the Horizon Shares and H-Lines Shares and (vii) a notation will be made in the appropriate records of Horizon and H-Lines indicating that the Horizon Shares and H-Lines Shares are subject to restrictions on transfer and, if either Horizon or H-Lines should at some time in the future engage the services of a stock transfer agent, appropriate stop-transfer restrictions will be issued to such transfer agent with respect to the Horizon Shares and H-Lines Shares.

(c) Such Optionholder hereby covenants that if any Horizon Shares or H- Lines Shares are disposed of by it (i) in reliance upon Rule 144 under the Securities Act, such Optionholder shall deliver to Horizons or H-Lines, as applicable, at or prior to the time of such

3

disposition an executed copy of Form 144 (if required by Rule 144) and such other documentation as either Horizons or H-Lines, as applicable, may reasonably require in connection with such disposition or (ii) in reliance on Rule 144 or pursuant to another exemption from registration under the Securities Act, Optionholder shall deliver to Horizons or H-Lines, as applicable, a legal opinion, reasonably satisfactory to Horizons or H-Lines, as to the availability of and compliance with such exemption.

(d) Such Optionholder represents and warrants that (i) it can afford to hold Horizon Shares and H-Lines Shares for an indefinite period and to suffer the complete loss of its investment in Horizon Shares and H-Lines Shares, (ii) it understands and has taken cognizance of all the risk factors related to its acquisition of Horizon Shares and H-Lines Shares and (iii) its knowledge and experience in financial and business matters is such that it is capable of evaluating the merits and risks of acquiring Horizon Shares and H-Lines Shares.

(e) Such Optionholder will be the record and beneficial owner of the Horizon Shares issued upon the exercise of Optionholder’s Roll-Over Options, and such Optionholder will hold the Horizon Shares free and clear of all security interests, liens, claims, pledges, options, rights of first refusal, contracts, limitations on such Optionholder’s voting rights, charges and other encumbrances of any nature whatsoever, except for the Call Right as contemplated by this Agreement and the Horizon Voting Trust Agreement, and such Horizon Shares will have been duly authorized and will be validly issued, fully-paid and non-assessable.

(f) If H-Lines or Horizons desires to register any Horizon Shares or H-Lines Shares pursuant to Form S-8, Optionholder acknowledges that any H-Lines Shares or Horizons Shares acquired may become subject to a “stock purchase plan” to facilitate such registration, provided that the terms of such stock purchase plan are consistent with the provisions of this Agreement. Such Optionholder hereby agrees, if requested by H-Lines or Horizons, to approve the terms of such stock purchase plan as it may be established at such time.

4. Representations and Warranties of H-Lines. H-Lines hereby represents and warrants to each Optionholder as follows:

(i) The authorized capitalization of H-Lines as of the date hereof consists of (A) 18,000,000 shares of Non-Voting Redeemable Preferred Stock, par value one cent ($0.01) per share (the “H-Lines Preferred Stock”) and (B) 2,000,000 shares of Common Stock, par value one cent ($0.01) per share (the “H-Lines Common Stock”), of which                  shares of H-Lines Preferred Stock are issued and outstanding and                  shares of H-Lines Common Stock are issued and outstanding.

(ii) H-Lines Shares being reserved hereunder by H-Lines have been duly authorized and will, upon consummation, from time to time, of the transactions contemplated herein, be validly issued, fully-paid and non-assessable.

5. Further Action. Each party hereto agrees to execute and deliver any instrument and take any action that may reasonably be requested by any other party for the purpose of effectuating the provisions of this Agreement.

4

6. Stock Legend. The Parties hereby agree that each certificate representing Horizon Shares issued to any Optionholder shall bear the following legend:

THE SECURITIES OF THE COMPANY REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO A PUT/CALL AGREEMENT AND A STOCKHOLDERS AGREEMENT, EACH DATED AS OF JULY 7, 2004, WHICH CONTAIN PROVISIONS REGARDING RESTRICTIONS ON THE TRANSFER OF SUCH SECURITIES AND OTHER MATTERS. COPIES OF SUCH AGREEMENTS ARE AVAILABLE FOR INSPECTION AT THE PRINCIPAL OFFICE OF THE COMPANY. THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), AND MAY NOT BE SOLD, TRANSFERRED OR ASSIGNED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION UNDER THE SECURITIES ACT OR IN A TRANSACTION EXEMPT FROM REGISTRATION UNDER THE SECURITIES ACT, IN EACH CASE IN ACCORDANCE WITH ANY APPLICABLE SECURITIES LAWS OF ANY STATE.

7. Miscellaneous Provisions.

(a) Assignability; Binding Effect. Except as otherwise provided in this Section, no right under this Agreement shall be assignable and any attempted assignment in violation of this provision shall be void. H-Lines shall have the right to assign its rights and obligations hereunder to any successor entity (including any entity acquiring substantially all of the assets of H-Lines), whereupon references herein to H-Lines shall be deemed to be to such successor. This Agreement, and the rights and obligations of the parties hereunder, shall be binding upon and inure to the benefit of any and all successors, permitted assigns, personal representatives and all other legal representatives, in whatsoever capacity, by operation of law or otherwise, of the parties hereto, in each case with the same force and effect as if the foregoing persons were named herein as parties hereto.

5

(b) Notices. Any notice or other communication required or which may be given hereunder shall be in writing and shall be delivered personally, telecopied with confirmed receipt, sent by certified, registered, or express mail, postage prepaid, or sent by a national next- day delivery service to the parties at the following addresses or at such other addresses as shall be specified by the parties by like notice, and shall be deemed given when so delivered personally or telecopied, or if mailed, 2 days after the date of mailing, or, if by national next-day delivery service, on the day after delivery to such service as follows:

if to H-Lines, to it at:

c/o Castle Harlan, Inc.

150 East 58^th Street

37^th Floor

New York, New York 10155

Attention: Marcel Fournier

Telecopier No.: 212 ###-###-####

with a copy to:

Castle Harlan, Inc.

150 East 58^th Street

37^th Floor

New York, New York 10155

Attention: Howard Weiss

Telecopier No.: 212 ###-###-####

and to:

Schulte Roth & Zabel LLP

919 Third Avenue

New York, NY 10022

Attention: André Weiss, Esq.

Telecopier No.: 212 ###-###-####

If to an Optionholder, to it at its address set forth under its signature page hereto.

(c) Applicable Law; Consent. This Agreement and the validity and performance of the terms hereof shall be governed by and construed in accordance with the laws of the State of New York without regard to principles of conflicts of law or choice of law. The parties hereto hereby agree that all actions or proceedings arising directly or indirectly from or in connection with this Agreement shall be litigated only in the Supreme Court of the State of New York or the United States District Court for the Southern District of New York located in New York County, New York. To the extent permitted by applicable law, the parties hereto consent to the jurisdiction and venue of the foregoing courts and consent that any process or notice of motion or other application to either of said courts or a judge thereof may be served inside or outside the State of New York or the Southern District of New York by registered mail, return receipt requested, directed to such party at its address set forth in this Agreement (and service so made shall be deemed complete five days after the same has been posted as aforesaid) or by personal service or in such other manner as may be permissible under the rules of said courts.

(d) Entire Agreement; Amendments and Waivers. This Agreement sets forth the entire understanding of the parties with respect to the subject matter hereof. The failure of any party to seek redress for the violation of or to insist upon the strict performance of any term of this Agreement shall not constitute a waiver of such term and such party shall be entitled to

6

enforce such term without regard to such forbearance. This Agreement may be amended only by the written consent of each party hereto, and each party hereto may take any action herein prohibited or omit to take action herein required to be performed by it, and any breach of or compliance with any covenant, agreement, warranty or representation may be waived only by the written waiver of the party against whom such action or inaction may negatively affect, but, in any case, such consent or waiver shall only be effective in the specific instance and for the specific purpose for which given.

(e) Headings. The headings in this Agreement are for reference purposes only and shall not in any way affect the meaning or interpretations of the Agreement.

(f) Severability. If any term, provision, covenant or restriction of this Agreement, or any part thereof, is held by a court of competent jurisdiction or any foreign federal, state, county or local government or any other governmental, regulatory or administrative agency or authority to be invalid, void, unenforceable or against public policy for any reason, the remainder of the terms, provisions, covenants and restrictions of this Agreement shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

(g) Counterparts. This Agreement may be executed in two or more counterparts, each of which shall be deemed an original, but all of which shall constitute one and the same instrument, and it shall not be necessary in making proof of this Agreement to produce or account for more than one such counterpart.

(h) Specific Performance. Each of the parties hereto acknowledges and agrees that in the event of any breach of this Agreement, the non-breaching party would be irreparably harmed and could not be made whole by monetary damages. It is accordingly agreed that the parties hereto shall and do hereby waive the defense in any action for specific performance that a remedy at law would be adequate and that the parties hereto, in addition to any other remedy to which they may be entitled at law or in equity, shall be entitled to compel specific performance of this Agreement in any action instituted in the Supreme Court of the State of New York or the United States District Court for the Southern District of New York, or, in the event such courts shall not have jurisdiction of such action, in any court of the United States or any state thereof having subject matter jurisdiction of such action.

(i) Survival of Covenants. All covenants, agreements, representations and warranties made herein or in any other document referred to herein or delivered to a party pursuant hereto or in connection herewith shall survive the execution and delivery to such party of this Agreement and of the H-Lines Shares.

[Remainder of page intentionally left blank]

7

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

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

[Signature Page of the Optionholders]

[Signature Page to Put/Call Agreement]

ANNEX 1

[Signature Page to Put/Call Agreement]