Inclusion Criteria:

          -  Patients with histologically or cytologically confirmed, epithelial ovarian, primary
             peritoneal or fallopian tube cancer who experienced recurrence or progression within
             12 months after completion of platinum based chemotherapy; patients must have
             measurable disease or detectable disease:

               -  Measurable disease is defined as at least one lesion that can be accurately
                  measured in at least one dimension (longest dimension to be recorded); each
                  lesion must be greater than or equal to 10 mm when measured by computerized
                  tomography (CT), positron emission tomography (PET)/CT or magnetic resonance
                  imaging (MRI); lymph nodes must be greater than or equal to 15 mm in short axis
                  when measured by CT, PET/CT or MRI

               -  Detectable disease in a patient is defined as one who does not have measurable
                  disease, but has at least one of the following conditions:

                    -  Baseline values of cancer antigen-125 (CA-125) at least 2 x upper limit of
                       normal (ULN)

                    -  Ascites and/or pleural effusion attributed to tumor

                    -  Solid and/or cystic abnormalities on radiographic imaging that do not meet
                       modified Response Evaluation Criteria In Solid Tumors (RECIST) criteria,
                       immune-related response criteria (irRC) for target lesions

          -  Patients whose ovarian cancer recurs/progresses within 0-6 months following
             platinum-based chemotherapy have platinum resistant disease; such patients are
             eligible for this trial

          -  Patients with documented disease recurrence/progression within 6-12 months of
             completing platinum-based therapy, are considered to have 'borderline' platinum
             sensitivity; these patients are eligible for this trial if agreed by the patient and
             the treating physician

          -  Patients who relapse more than 12 months after completion of platinum-based treatment
             are considered 'platinum sensitive' and will not be eligible for this trial

          -  Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status =<
             2 (Karnofsky >= 60%)

          -  Patients must have a life expectancy of at least 3 months

          -  Absolute neutrophil count >= 1,500/ul

          -  Platelets >= 100,000/ul; low platelet counts may be corrected with transfusion to
             achieve eligibility for study

          -  The hemoglobin level must be greater than 9 g/dL; low hemoglobin counts may be
             corrected with transfusion to achieve eligibility for study

          -  Calculated or measured creatinine clearance >= 50 ml/min or serum creatinine =< 1.6
             mg/dl

          -  Total bilirubin =< 1.5 x institutional upper limit of normal

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 3 times
             institutional upper normal level (AST and ALT =< 5 times institutional upper normal
             level, if there is evidence of liver metastasis)

          -  Women of childbearing potential must agree to use adequate contraception (hormonal or
             barrier method of birth control or abstinence) prior to study entry and for six months
             following duration of study participation; should a woman become pregnant or suspect
             that she is pregnant while participating on the trial, she should inform her treating
             physician immediately

          -  Patients with confirmed p53 mutation by molecular analysis and/or evidence of p53
             overexpression by immunohistochemistry (IHC) (>= 10% of cells within the tumor
             staining positive) will be eligible; this will be assessed semi-quantitatively by a
             Clinical Laboratory Improvement Amendments (CLIA) approved pathology core pathologist,
             using CLIA approved mutational analysis or immunohistochemistry techniques on
             formalin-fixed paraffin-embedded tissue; in the case of equivocal IHC results, p53
             involvement may be confirmed by detection of p53 molecular analysis on tumor
             deoxyribonucleic acid (DNA); patients on whom molecular analysis of p53 mutations is
             already available, will not require IHC analysis; molecular analysis may be performed
             as an additional research procedure at the end of the study (distinct from eligibility
             determination) if the principal investigator (PI) deems it of scientific value and
             research funding is available to cover the cost

          -  All subjects must have the ability to understand and the willingness to sign a written
             informed consent

          -  Up to 2 prior chemotherapy regimens for recurrent disease are allowed; adjuvant
             chemotherapy and maintenance Taxol after completion of six cycles of adjuvant
             carboplatin

          -  Taxol will not be counted as a "prior chemotherapy regimen" for the purpose of this
             study; treatment with targeted agents or hormones would not be considered as a
             systemic chemotherapy regimen; previous treatment with gemcitabine is not allowable

          -  Eligible patients are those with documented disease recurrence/progression within 0-12
             months of completing platinum-based chemotherapy

        Exclusion Criteria:

          -  Patients should not have any uncontrolled illness including ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements

          -  No other malignancy is allowed except for the following: adequately treated basal or
             squamous cell carcinoma, superficial bladder cancer, any carcinoma in situ or any
             other cancer from which the patient has been disease free for at least 3 years

          -  Patients may not be receiving any additional investigational agents or radiation
             therapy

          -  History of severe environmental allergies or allergy to egg proteins

          -  Pregnant women are excluded from this study

          -  Patients with known brain metastases will be excluded

          -  Patients who have had radiotherapy within 4 weeks prior to entering the study or those
             who have not recovered from adverse events due to agents administered more than 4
             weeks earlier

          -  Patients with a family history or Li-Fraumeni syndrome will not be eligible

          -  Concurrent use of corticosteroids (exceptions: nasal corticosteroids, inhaled
             steroids, adrenal replacement steroids and steroid creams are allowed)

          -  Patients with a history of immunodeficiency, including organ grafts and human
             immunodeficiency virus (HIV), will not be eligible

          -  Subjects, who in the opinion of the investigator, may not be able to comply with the
             safety monitoring requirements of the study

          -  Patients with any active autoimmune disease or a condition that requires systemic
             corticosteroids or other immunosuppressive medications will be excluded; exceptions to
             this are subjects with vitiligo, type I diabetes mellitus and autoimmune thyroiditis
             only requiring hormone replacement, who will be permitted to enroll