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.