Exhibit 1.4

Amendment to On Demand Sales Agreement

Dated as of September 4, 2015

JMP Securities LLC

600 Montgomery Street, 11th Floor

San Francisco, CA 94111

Ladies and Gentlemen:

Reference is hereby made to the on demand sales agreement, dated September 6, 2013 (the “Original JMP On Demand Sales Agreement”), among Chesapeake Lodging Trust, a real estate investment trust organized under the laws of the state of Maryland (the “Company”), Chesapeake Lodging, L.P, a Delaware limited partnership and the operating partnership of the Company (the “Operating Partnership”), and JMP Securities LLC (the “Agent”). This amendment to the Original JMP On Demand Sales Agreement is referred to as the “Amendment.” The Company and the Operating Partnership also entered in an on demand sales agreement with Robert W. Baird & Co. Incorporated, dated September 6, 2013 (the “Original Baird On Demand Sales Agreement”).

Capitalized terms used herein and not defined have the respective meanings set forth in the Original JMP On Demand Sales Agreement.

The Original JMP On Demand Sales Agreement relates to the offering and sale of up to $100,000,000 of Shares pursuant to the Company’s registration statement on Form S-3 (File No. 333-183280). The Company has prepared and filed with the Commission (i) an automatic shelf registration statement on Form S-3 (File No. 333-198558) relating to, among other things, the offering and sale of the Company’s Common Shares (which new registration statement became effective upon the filing thereof with the Commission on September 3, 2014) (the “New Registration Statement”), (ii) an accompanying prospectus, dated September 3, 2014 (the “New Base Prospectus”) and (iii) a prospectus supplement dated, September 4, 2015 (the “New Prospectus Supplement”), relating to the Shares.

The parties desire to amend the Original JMP On demand Sales Agreement as follows:

“The Company meets the requirements for use of Form S-3 under the Act and has prepared and filed with the Commission a registration statement on Form S-3 (File Number 333-198558), including a related Base Prospectus, for registration under the Act of the offering and sale of certain securities, including the Shares. Such Registration Statement, including any amendments thereto filed prior to the Execution Time or prior to any such time this representation is repeated or deemed to be made, has become effective under the Act. Such Registration Statement is an “automatic shelf registration statement” as defined under Rule 405 of the Act that has been filed with the Commission not earlier than three years prior to the Execution Time; and no notice of objection of the Commission to the use of such registration statement has been received by the Company and no post-effective amendment thereto pursuant to Rule 401(g)(2) under the Securities Act has been filed as of the Execution Time. The Company has filed with the Commission the Prospectus Supplement relating to the Shares in accordance with Rule 424(b). As filed, the Prospectus contains all information required by the Act and the rules thereunder, and, except to the extent JMP shall agree in writing to a modification, shall be in all substantive respects in the form furnished to JMP prior to the Execution Time. The Registration Statement meets at the Execution Time, and will meet at each subsequent time this representation is repeated or deemed to be made, and at all times during which a prospectus is required by the Act to be delivered (whether physically or through compliance with Rule 172 or any similar rule) in connection with any offer or sale of Shares, the requirements set forth in Rule 415(a)(1)(x). The initial Effective Date of the Registration Statement was not earlier than the date three years before the Execution Time. Any reference herein to the Registration Statement, the Base Prospectus, the Prospectus Supplement or the Prospectus shall be deemed to refer to and include the documents incorporated or deemed to be incorporated by reference therein as of the time of such reference. The Company has paid any required registration fee for the Shares within the time period required by Rule 456(b)(1) under the Act (without giving effect to the proviso therein).”

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“(i) At the earliest time after the filing of the Registration Statement that the Company or another offering participant made a bona fide offer (within the meaning of Rule 164(h)(2)) of the Shares and (ii) as of the Execution Time and on each such time this representation is repeated or deemed to be made (with such date being used as the determination date for purposes of this clause (ii)), the Company (A) was not and is not an Ineligible Issuer and (B) was and is a “well-known seasoned issuer” (in each case, as defined in Rule 405).”

“During any period when the delivery of a prospectus relating to the Shares is required (including in circumstances where such requirement may be satisfied pursuant to Rule 172) under the Act, the Company will not file any amendment to the Registration Statement or supplement (including the Prospectus Supplement) to the Base Prospectus unless the Company has furnished to JMP a copy for its review prior to filing and will not file any such proposed amendment or supplement to which JMP reasonably objects, except for a supplement relating to an offering of the Company’s securities other than the Shares. The Company will cause any supplement to the Prospectus to be properly completed, in a form approved by JMP, and will file such supplement with the Commission pursuant to the applicable paragraph of Rule 424(b) within the time period prescribed thereby and will provide evidence satisfactory to JMP of such timely filing. The Company will promptly advise JMP (i) when the Prospectus, and any supplement thereto, shall have been filed (if required) with the Commission pursuant to Rule 424(b), (ii) when, during any period when the delivery of a prospectus (whether physically or through compliance with Rule 172 or any similar rule) is required under the Act in connection with the offering or sale of the Shares, any amendment to the Registration Statement shall have been filed or become effective, (iii) of any request by the Commission or its staff for any amendment of the Registration Statement, or any Rule 462(b) Registration Statement, or for any supplement to the Prospectus or for any additional information, (iv) of the issuance by the Commission of any stop order suspending the effectiveness of the Registration Statement or of any notice objecting to its use or the institution or threatening of any proceeding for that purpose, (v) of the receipt by the Company of any notice of objection of the Commission to the use of the Registration Statement or any post-effective amendment thereto pursuant to Rule 401(g)(2) under the Securities Act, and (vi) of the receipt by the Company of any notification with respect to the suspension of the qualification of the Shares for sale in any jurisdiction or the institution or threatening of any proceeding for such purpose. The Company will use its best efforts to prevent the issuance of any such stop order or the occurrence of any such suspension or objection to the use of the Registration Statement and, upon such issuance, occurrence or notice of objection, to obtain as soon as possible the withdrawal of such stop order or relief from such occurrence or objection, including, if necessary, by filing an amendment to the Registration Statement or a new registration statement and using its best efforts to have such amendment or new registration statement declared effective as soon as practicable.”

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If the foregoing is in accordance with your understanding of our agreement, please sign and return to the Company and the Operating Partnership a counterpart hereof, whereupon this agreement, along with all counterparts, will become a binding agreement among the Agent, the Company and the Operating Partnership in accordance with its terms.

Signature Page