Inclusion Criteria:

          -  Participants must have histologically confirmed epithelial ovarian, fallopian tube, or
             primary peritoneal cancer.

          -  Participants must have completed at least first-line platinum based chemotherapy and
             surgery with a response, in the opinion of the investigator, defined as no evidence of
             disease progression or rising CA-125 at any time during front-line treatment.

          -  Participants must meet criteria for tumor marker-only relapse, defined as CA-125 more
             than twice the upper limit of normal (35 U/mL) in the setting of a normal baseline
             CA-125 levels or CA-125 greater than twice the nadir count on two successive
             measurements for CA-125 values that remain above baseline without measurable
             radiographic disease.

          -  Minimum age ≥ 18 years. Because no dosing or adverse event data are currently
             available on the use of zafirlukast in participants under 18 years of age with ovarian
             cancer, children are excluded from this study but will be eligible for future
             pediatric trials.

          -  Life expectancy of greater than 4 months.

          -  ECOG performance status ≤ 2 (Karnofsky ≥ 60%, see Appendix A).

          -  Participants must be able to swallow tablets.

          -  Participants must have adequate organ and marrow function as defined below:

               -  Absolute neutrophil count ≥1,000/mcL

               -  Platelets ≥100,000/mcL

               -  Total bilirubin ≤ 1.3 × institutional upper limit of normal (ULN)

               -  AST(SGOT)/ALT(SGPT) ≤ 2 × institutional ULN

               -  Creatinine ≤ institutional ULN OR

               -  Glomerular filtration rate (GFR) ≥45 mL/min/1.73 m2

          -  The effects of zafirlukast on the developing human fetus are incompletely
             characterized. For this reason, women of child-bearing potential must agree to use
             adequate contraception (hormonal or barrier method of birth control; abstinence) prior
             to study entry and for the duration of study participation. Should a woman become
             pregnant or suspect she is pregnant while she or her partner is participating in this
             study, she should inform her treating physician immediately. Men are not eligible for
             this study.

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  Non-epithelial tumors (pure sarcomas) or ovarian tumors with low malignant potential
             (ie borderline tumors) or mucinous tumors. Mixed mullerian tumors or carcinosarcomas
             are allowed.

          -  Participants who have had cytotoxic chemotherapy including bevacizumab or radiotherapy
             within 4 weeks prior to entering the study. This does not include maintenance therapy
             (>8 weeks prior to enrollment of stable dose) with a PARP inhibitor, such as olaparib
             or niraparib. (PARP inhibitor, rucaparib is not allowed to be co-administered with
             CYP2C9 substrates as maintenance therapy as it could increase exposure to
             zafirlukast).

          -  Participants who have ongoing adverse effects from prior anti-cancer therapy greater
             than National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events
             (CTCAE, v5.0) Grade 1, with the exception of Grade 2 non-hematologic toxicity such as
             alopecia and peripheral neuropathy.

          -  Participants who are receiving any other investigational agents.

          -  Participants with known brain metastases should be excluded from this clinical trial
             because of their poor prognosis and because they often develop progressive neurologic
             dysfunction that would confound the evaluation of neurologic and other adverse events.

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to zafirlukast.

          -  Currently receiving anticoagulant therapy.

          -  Current daily use of aspirin (> 81 mg daily), clopidogrel (Plavix), cilostazol
             (Pletal), aspirin-dipyridamole (Aggrenox) (within 10 days) or considered to use
             regular use of higher doses of non-steroidal anti-inflammatory agents as determined by
             the treating physician (e.g. ibuprofen > 800 mg daily or equivalent).

          -  Participants receiving any medications or substances that are inhibitors or inducers
             of CYP2C9 are ineligible. Because the lists of these agents are constantly changing,
             it is important to regularly consult a frequently updated medical reference. As part
             of the enrollment/informed consent procedures, the participant will be counseled on
             the risk of interactions with other agents, and what to do if new medications need to
             be prescribed or if the participant is considering a new over-the-counter medicine or
             herbal product.

          -  Participants with uncontrolled intercurrent illness.

          -  Participants with psychiatric illness/social situations that would limit compliance
             with study requirements.

          -  Pregnant women are excluded from this study because zafirlukast is a class B agent
             with the potential for teratogenic or abortifacient effects. Because there is an
             unknown but potential risk for adverse events in nursing infants secondary to
             treatment of the mother with zafirlukast, breastfeeding should be discontinued if the
             mother is treated with zafirlukast.