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                                                                    Exhibit 10.4

300,000 SHARES OF COMMON STOCK                          GRANT DATE: MAY 27, 2004

                           SYNTA PHARMACEUTICALS CORP.

                      NON-QUALIFIED STOCK OPTION AGREEMENT

     SYNTA PHARMACEUTICALS CORP., a Delaware corporation (the "Company"), grants
to KEITH R. GOLLUST (the "Optionee"), as of the date set forth above, the right
and option (this "Option") to purchase from the Company up to 300,000 shares
(the "Option Shares") of the Common Stock, $.000l par value, of the Company (the
"Common Stock"). This Option is subject to the following terms and conditions:

     1.   OPTION PRICE. The price to be paid for each share of Common Stock upon
exercise of the whole or any part of this Option shall be $2.7108 (the "Purchase
Price").

     2.   VESTING. This Option shall be exercisable with respect to 150,000
shares of the Option Shares as of the Grant Date, and the remainder of the
Option Shares will become exercisable thereafter in eight equal cumulative
quarterly installments of 18,750 shares, the first such installment occurring on
August 27, 2004, PROVIDED THAT Optionee on the applicable installment date is
providing services to the Company as a director, advisor or consultant. If the
Optionee is granted the right to receive any new, substituted or additional
securities or other property (including money paid other than as a regular cash
dividend) pursuant to Section 6, then such new or substituted securities
(together with the Option Shares, the "Option Securities") or other property
shall be issued upon the exercise of this Option subject to the same vesting
schedule applicable to this Option.

     3.   OPTION PERIOD. This Option shall terminate and be of no further force
or effect at 5:00 P.M., Boston time, on May 27, 2014.

     4.   EXERCISE OF OPTION; PAYMENT FOR SHARES. This Option may be exercised
at any time and from time to time, subject to the limitations of Sections 2 and
3 and set forth elsewhere in this Agreement, for up to the aggregate number of
shares of Option Securities specified herein, but in no event for the purchase
of other than whole shares. A written notice of exercise in the form of Exhibit
A attached hereto, signed by the Optionee or his heirs or permitted assignees
(the "Exercising Party"), shall be delivered to the Company at its principal
office specifying the number of Option Securities with respect to which this
Option is being exercised. Such notice shall be accompanied by this Agreement
and by payment of the purchase price of the Option Securities being acquired,
which payment may be (a) in United States dollars in cash, by check or by wire
transfer to a deposit account specified by the Company, (b) at the discretion of
the Company, through delivery to the Company of shares of its capital stock held
by the Exercising Party for at least six (6) months prior to the exercise of
this Option or retention by the Company of shares otherwise issuable upon
exercise of this Option, in each case having a Fair Market Value (as defined in
Section 7 below) as of the date of exercise equal to the number of exercised
shares multiplied by the Purchase Price, (c) at the discretion of the Company,
in accordance with a cashless exercise program established with a securities
brokerage firm, or (d) by any combination of (a), (b), or (c) above.

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     5.   NO RIGHTS AS STOCKHOLDERS NO RIGHT TO CONTINUING RELATIONSHIP. The
Optionee shall not be deemed, for any purpose, to have any rights whatsoever
with respect to Option Securities to which this Option shall not have been
exercised and payment made as aforesaid. The Optionee shall have no rights as a
stockholder with respect to shares of Option Securities until the date of
issuance of such shares. No adjustment shall be made for dividends (ordinary or
extraordinary, whether in cash, securities or other property) or distributions
or other rights for which the record date is prior to the date such Option
Securities are issued, except as provided in Section 6. The Optionee shall not
be deemed to have any rights to a continued relationship with the Company by
virtue of the grant or exercise of this Option. The Optionee acknowledges that
he has no right to continue as a director, advisor or consultant of the Company
and that the Company, its Board, and/or its shareholders may terminate or remove
the Optionee from his position as a director, advisor, or consultant with or
without reason or cause at any time so long as such action to terminate or
remove is in accordance with the Company's by-laws and applicable law.

     6.   EXTRAORDINARY EVENTS. Upon the occurrence of any of the following
events, the Optionee's rights with respect to the Option Securities shall be
adjusted as hereinafter provided:

          (a)  STOCK DIVIDENDS AND STOCK SPLITS. If (i) the shares of the
Company's Common Stock shall be subdivided or combined into a greater or smaller
number of shares or if the Company shall issue any shares of Common Stock as a
stock dividend on its outstanding Common Stock, or (ii) additional shares or new
or different shares or other securities of the Company or other non-cash assets
are distributed with respect to such shares of Common Stock, the number of
shares of Common Stock deliverable upon the exercise of the Optionee's rights
pursuant to this Option shall be appropriately increased or decreased
proportionately, and appropriate adjustments may be made in the purchase price
per share to reflect such events.

          (b)  CONSOLIDATIONS OR MERGERS. If the Company is to be consolidated
with or acquired by another entity in a merger, sale of all or substantially all
of the Company's assets or otherwise (an "Acquisition"), the Board of Directors
of any entity assuming the obligations of the Company hereunder, shall either
(i) make appropriate provision for the continuation of this Option by
substituting on an equitable basis for the Option Securities either the
consideration payable with respect to the outstanding shares of Common Stock in
connection with the Acquisition or securities of any successor or acquiring
entity; or (ii) upon written notice to the Optionee, provide that the Option
must be exercised (either to the extent then exercisable or, at the discretion
of the Board of Directors, all Option Securities being made fully exercisable
for purposes of this subparagraph) prior to a specified date at the end of which
period this Option shall terminate; or (iii) terminate this Option in exchange
for a cash payment equal to the excess of the Fair Market Value of the Option
Securities (either to the extent then exercisable or, at the discretion of the
Board of Directors, all Option Securities being made fully exercisable for
purposes of this subparagraph) over the exercise price thereof.

          (c)  RECAPITALIZATION OR REORGANIZATION. In the event of a
recapitalization or reorganization of the Company (other than a transaction
described in subparagraph (b) above) pursuant to which securities of the Company
or of another corporation are substituted or exchanged for the outstanding
shares of Common Stock, the Optionee upon exercising the

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Option shall be entitled to receive for the Purchase Price the securities which
would have been received if this Option had been exercised prior to such
recapitalization or reorganization.

     7.   FAIR MARKET VALUE. The fair market value ("Fair Market Value") of the
Option Securities for purposes of this Option shall be an amount per share
determined as follows:

          (1)  If the Option Securities are listed on a national securities
     exchange or traded in the over-the-counter market and sales prices are
     regularly reported for the Option Securities, the per share fair
     market value shall be the closing or last price of the Option
     Securities on the composite tape or other comparable reporting system
     for the trading day immediately preceding the applicable date;

          (2)  If the Option Securities are not traded on a national
     securities exchange but are traded on the over-the-counter market, if
     sales prices are not regularly reported for the Option Securities for
     the trading day referred to in clause (1), and if bid and asked prices
     for the Option Securities are regularly reported, the per share fair
     market value shall be the mean between the bid and the asked price for
     the Option Securities at the close of trading in the over-the-counter
     market for the trading day on which Option Securities were traded
     immediately preceding the applicable date; and

          (3)  If the Option Securities are neither listed on a national
     securities exchange nor traded in the over-the-counter market, the per
     share fair market value shall be such value as the Company's Board of
     Directors, in good faith, shall determine.

     8.   NON-ASSIGNABILITY OF OPTION RIGHTS. Except as set forth below, the
Option shall (a) not be assignable or transferable by the Optionee, either
voluntarily or by operation of law, except by will or the laws of descent and
distribution; (b) be exercisable only by the Optionee during the life of the
Optionee; and (c) not be transferred, assigned, pledged, hypothecated or
disposed of in any other way (whether by operation of law or otherwise), or be
subject to execution, attachment or similar process. Notwithstanding the
foregoing, the Optionee may upon written notice to the Company at any time
assign or transfer the Option to a tax exempt organization as defined in
Section501(c)(3) of the United States Internal Revenue Code of 1986, as amended
(the "Code"), to a private foundation as defined in Section509(a) of the Code,
or to a charitable remainder trust under Section664 of the Code, provided that:

          (i)   such transferee shall automatically be bound by the terms of
     this Option;
          (ii)  if requested, Optionee shall provide the Company with reasonable
     documentation verifying the federal tax exempt status of such transferee;
     and
          (iii) if this Option terminates for any reason, the Optionee or his
     personal representative shall give notice to such transferee of such
     termination.

     9.   INVESTMENT REPRESENTATION; COMPLIANCE WITH LISTING REQUIREMENTS AND
LAW. The Optionee, by acceptance of this Option, hereby represents and warrants
that this Option and any and all shares of the Option Securities which the
Optionee shall acquire upon the exercise of this Option are being and will be
acquired for his own account for investment and not with a view to, or for sale
in connection with, any distribution thereof. It shall be a condition to the
Optionee's right to purchase the Option Securities that the Company may require
such steps or satisfaction

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of such conditions as the counsel for the Company may reasonably deem necessary
to comply with any law, rule or regulation applicable to the issuance of such
Option Securities, including, without limitation, (a) that the Option Securities
reserved for issue upon the exercise of this Option shall have been duly listed,
upon official notice of issuance, upon any national securities exchange on which
the Option Securities may then be listed, and (b) that either (i) a registration
statement under the Securities Act of 1933, as amended (the "Act"), and the
rules and regulations promulgated thereunder with respect to such shares shall
be in effect or (ii) in the opinion of counsel for the Company the proposed
purchase shall be exempt from registration under the Act and the Optionee shall
have made such undertakings and agreements with the Company as the Company may
reasonably require. The certificates representing the shares of Option
Securities purchased under this Option may contain such legends as counsel for
the Company shall deem necessary to comply with such applicable law, rule or
regulation.

     The exercise of this Option shall be subject to the requirement that if, at
any time, counsel to the Company shall determine that the listing, registration
or qualification of the Option Securities upon any securities exchange or under
any state or federal law, or the consent or approval of any governmental or
regulatory body, or that the disclosure of non-public information or the
satisfaction of any other condition is necessary as a condition of, or in
connection with, the issuance or purchase of the Option Securities, such shares
may not be issued or this Option exercised, in whole or in part, unless such
listing, registration, qualification, consent or approval, or satisfaction of
such condition shall have been effected or obtained on conditions acceptable to
the Company. Nothing herein shall be deemed to require the Company to apply for
or to obtain such listing, registration or qualification, or to satisfy such
condition.

     10.  PAYMENT OF TAXES.

          (a)  The Company's obligation to deliver the Option Securities upon
the exercise of this Option shall be subject to the satisfaction by the
Exercising Party of all applicable federal, state and local income and
employment tax withholding requirements.

          (b)  Upon the exercise of this Option, the Exercising Party shall pay
to the Company, or authorize it to deduct from other amounts payable to the
Exercising Party, the amount of any taxes that the Company or any of its
subsidiaries is required to withhold with respect to such exercise. Subject to
the prior approval of the Company, which may be withheld by the Company in its
discretion, the Exercising Party may elect to satisfy such obligations, in whole
or in part, by (i) causing the Company to withhold shares of the Option
Securities otherwise issuable pursuant to the exercise of this Option, or (ii)
delivering to the Company, at the time this Option is exercised, shares of the
Company's capital stock held by the Exercising Party for at least six (6) months
prior to the exercise of the Option. The shares of the Company's capital stock
so delivered or withheld shall have a Fair Market Value equal to such
withholding obligation. The Fair Market Value of the shares of the Company's
capital stock used to satisfy such withholding obligation shall be determined by
the Company as of the date that the amount of tax to be withheld is to be
determined.

          (c)  Notwithstanding the foregoing, in the event that the Exercising
Party is a person required to file reports under Section 16(a) of the Securities
Exchange Act of 1934, as amended, no election to use shares of the Company's
capital stock for the payment of

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withholding taxes shall be effective unless made in compliance with any
applicable requirement of Rule 16b-3 (unless it is intended that the transaction
not qualify for exemption under Rule 16b-3).

     11.  MISCELLANEOUS. This Option may not be altered or amended except by a
written instrument signed by the Company and the Optionee. This Option contains
the entire agreement and understanding between the Company and the Optionee with
respect to the subject matter hereof, and supersedes all prior or
contemporaneous agreements or understandings. This Option shall be governed by
and construed in accordance with the laws of the State of Delaware, without
regard to any conflict of laws principles. If any provision of this Option shall
be determined to be illegal and unenforceable, the remaining provisions shall be
severable and enforceable in accordance with their terms. All the terms and
provisions of this Option shall be binding upon and inure to the benefit of the
parties hereto and, subject to the terms and provisions of Section 8 their
respective heirs, legal representatives, successors and permitted assigns.

     IN WITNESS WHEREOF, the Company has caused this Option to be executed on
its behalf and its corporate seal to be hereunto affixed as of the date first
set forth above.


                                           SYNTA PHARMACEUTICALS CORP.


                                           By: /S/ DR. SAFI BAHCALL
                                               ---------------------------------
                                           Name: Dr. Safi Bahcall
                                           Title: President and Chief Executive
                                                  Officer


The undersigned hereby accepts and agrees to the terms and conditions contained
in this Option as of the date specified above.


                                           /S/ KEITH R. GOLLUST
                                           -------------------------------------
                                           KEITH R. GOLLUST

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EXHIBIT A

                                 EXERCISE NOTICE

Synta Pharmaceuticals Corp.
45 Hartwell Avenue
Lexington, MA 02421
Attn.: Chief Financial Officer

     This Exercise Notice is pursuant to a Non-Qualified Stock Option Agreement
dated as of May 27, 2004 (the "Option"), by and between Synta Pharmaceuticals
Corp. (the "Company") and Keith R. Gollust. Unless otherwise noted herein,
capitalized terms used in this Exercise Notice have the meanings set forth in
the Option. The undersigned, the recipient or permitted assignee of the
Optionee, hereby elects today to exercise the Option to purchase ____________
shares of the Option Securities of the Company (the "Purchased Shares"), and
with this Exercise Notice the undersigned is delivering to you one or more of
the following in payment of the aggregate exercise price for the shares (the
"Exercise Price"):

     (a)  $_____________ in cash, by personal check or by wire transfer;

     (b)  stock certificates for _____________ shares of the Company's capital
stock (the "Certificates") with a Fair Market Value of $________,accompanied by
duly executed stock power(s) for each Certificate; or

     (c)  notice of the undersigned's consent for the Company to retain
___________ shares of the Option Securities with a Fair Market Value of
$___________________ .

Accordingly, please issue a stock certificate for the shares in the
undersigned's name and have it delivered to the undersigned at the address
indicated below. Notwithstanding, the undersigned understands that the Company
may issue a stock certificate for less than the total number of Purchased Shares
in the event the Company withholds shares in order to satisfy any applicable
withholding tax obligation of the Company. The undersigned acknowledges his or
its responsibility to comply with the tax withholding requirements set forth in
Section 10 of the Option.

     The undersigned hereby acknowledge that he or it has been given the
opportunity to ask questions of, and to obtain such information from, the
Company as he or it deems necessary to evaluate the merits of making an
investment in the Option Securities of the Company.

     The undersigned hereby confirms that he or it is acquiring the Option
Securities for the undersigned's own account for investment and not with any
present intention of selling or otherwise distributing the shares, and the
undersign confirms that he or it will in no event sell, transfer, pledge or
otherwise dispose of the shares prior to (a) receipt of an opinion of counsel
for the Company authorizing any such proposed sale, transfer, pledge or other
disposition, (b) receipt of a "no action" letter from the Securities and
Exchange Commission or (c) registration of the Option Securities under the
Securities Act of 1933, as amended. The undersigned

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understands that the certificate representing the Option Securities will bear a
legend noting these restrictions on transferability.

                                      Dated:
--------------------------------            --------------------------
Print Name


--------------------------------
Signature

Address:
        ------------------------
--------------------------------

Social Security No. or E.I.N.:
                              -----------

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