The purpose of this study is to test the safety of a combination of an investigational WT1 vaccine and another drug called nivolumab. This is the first time that the WT1 vaccine and nivolumab are being used in combination. Also, to test the safety of a combination of an investigational NY-ESO-1 vaccine and another drug called nivolumab.

Inclusion Criteria:

• Pathologic diagnosis of ovarian, fallopian tube or primary peritoneal cancer confirmed by pathology review at MSK.
• Patients will have relapsed at least once and returned to complete clinical remission after additional chemotherapy. Interval surgery is permitted.
• Complete clinical remission is defined as CA-125 within normal limits, examination and CT or MRI without objective evidence of disease (non specific abnormalities are permitted on radiologic imaging).
• Patients may sign screening consent during recurrence or at time of remission if they can start vaccine therapy within 4 months of completing chemotherapy.
• Testing of patient's archived (paraffin embedded, unstained slides) or freshly biopsied tumor nodules must be positive for WT1 (Cohort 1) or NY-ESO-1 (Cohort 2) protein expression. WT1 expression: Immunohistochemical analysis will be performed using the technique described by Dupont et al [58]. WT1 expression will be graded according to an adaptation of the German Immunoreactive Score (IRS). Only tumors with moderate to strong IRS scores (4-12) will be considered WT1 positive.
• NY-ESO-1 expression: Tissue available from primary and/or recurrent disease will be evaluated for tumor expression of NY-ESO-1 by immunohistochemical (IHC) and/or RT-PCR analysis will be performed using the technique described by Jungbluth et al
• Age ≥ 18 years
• Karnofsky performance status ≥ 70%
• Hematologic parameters: Absolute neutrophil count ≥ 1000/mcL, Platelets > 50 K/mcL.
• Biochemical parameters: Total bilirubin ≤ 1.5 mg/dl, AST and ALT ≤ 2.5 x upper limits of normal, Creatinine ≤ 1.5 mg/dl.
• Patient of childbearing potential must have a negative serum pregnancy test prior to study entry and must be practicing and effective form of birth control

Exclusion Criteria:

• Pregnant or lactating women
• Patients with active infection requiring systemic antibiotics, antiviral, or antifungal treatments
• Patients with a serious unstable medical illness or another active cancer.
• Patients with a condition requiring systemic treatment with either corticosteroids (>10mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses >10mg daily prednisone equivalents are permitted in the absence of active autoimmune disease.
• Patients with known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS).
• Patients with known active hepatitis B virus or hepatitis C virus acute or chronic infection.
• Patients with active known or suspected autoimmune disease (treated hypothyroidism is permitted to enroll)
• Patients with active interstitial pneumonitis.