Study of Adjuvant Ipilimumab and Nivolumab in Subjects With High-risk Ocular Melanoma

Inclusion Criteria: 1. Written informed consent and HIPAA authorization for release of personal health information prior to registration. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. 2. Age ≥ 18 years at the time of consent. No dosing or adverse event data are currently available on the use of ipilimumab in combination with nivolumab in patients \< 18 years of age. 3. ECOG Performance Status of 0-1 within 28 days prior to registration. 4. Patients must have clinically confirmed ocular melanoma diagnosed by a retinal specialist or ocular oncologist. NOTE: Patients with cutaneous melanoma, acral melanoma, mucosal melanoma, or conjunctival melanoma are ineligible. 5. Patients must have ocular melanoma that is considered high-risk for recurrence as defined by one of the following criteria: * Gene Expression Profile using 15-gene panel (Castle Bioscience) and be classified as Class 2, or * 3-year recurrent risk of more than 50% as defined by Impact Genetics, or * Monosomy of chromosome 3 with apical tumor height \> 8mm (53). 6. The primary tumor measured at least 12mm in largest basal diameter as clinically determined by the site investigator. Size is based on clinical assessment (e.g. by ultrasound or direct ophthalmoscopy) prior to enucleation or radiation therapy. 7. Archival tumor tissue is required for subjects that have had enucleation; subjects that have had enucleation but do not have available archival tissue are not eligible for participation. Archival tissue is required if available for subjects that have not had enucleation; if not available these patients are still eligible. 8. Patients must have undergone an adequate treatment for the primary ocular melanoma deemed appropriate by the treating physician. 9. All participants must have been adequately treated for local disease and have documentation of distant/metastatic disease-free status by a complete physical examination and imaging studies within 4 weeks prior to registration. Imaging studies must include CT or MRI scans of the chest, abdomen, and pelvis. Brain MRI should be performed only as clinically indicated. 10. Patients must be registered within 180 days of the last treatment performed to render the patient free of disease. 11. Patient may have received prior radiation therapy to the primary site, including after the surgical resection. No systemic radiation for metastatic ocular melanoma is permitted. 12. Subject re-enrollment: This study permits the re-enrollment of a participant who has discontinued the study as a screen failure. If re-enrolled, the participant must be re-consented 13. Demonstrate adequate organ function as defined in the table below. All screening labs to be obtained within 28 days prior to registration. * Absolute Neutrophil Count (ANC) ≥ 1,500 cells/mm3 * Platelets ≥ 100,000 cells/mm3 * Hemoglobin (Hgb) ≥ 9 g/dL (NOTE: The use of transfusion or to achieve Hgb ≥ 10 g/dl is acceptable) * Serum creatinine ≤ 1.5 x institutional upper limit normal (IULN) OR eGFR \> 30mL/min for participant with creatinine levels \> 1.5 x ULN * Bilirubin ≤ 1.5 x IULN (except subjects with Gilbert Syndrome who can have total bilirubin ≥ 3.0 mg/dL) * Aspartate aminotransferase (AST) ≤ 3.0 x IULN * Alanine aminotransferase (ALT) ≤ 3.0 x IULN * Alkaline phosphatase ≤ 2.5 IULN 14. Neuropathy (sensory and motor) Grade ≤ 1 (CTCAE v4) 15. Females of childbearing potential must have a negative urine or serum pregnancy test at screening and within 24 hours prior to initiation of study treatment. Females must be willing to use contraception as outlined in the protocol. Male contraception is not required. 16. As determined by the enrolling physician or protocol designee, ability of the subject to understand and comply with study procedures for the entire length of the study 17. Subject re-enrollment: This study permits the re-enrollment of a participant who has discontinued the study as a screen failure. If re-enrolled, the participant must be re-consented. Exclusion Criteria: 1. Patients with evidence of distant metastases (stage IV ocular melanoma) are not eligible. 2. Patients with local or orbital recurrence are not eligible. 3. Patients with cutaneous, mucosal, acral or conjunctival melanoma are not eligible. 4. Subjects with active, known, or suspected autoimmune disease. Subjects with Type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis or alopecia) not requiring systemic treatment or conditions not expected to recur in the absences of an external trigger are permitted to enroll. 5. Subjects with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 2 weeks of study drug administration. Inhaled or topical steroids and adrenal replacement doses \< 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. 6. Participants with previous malignancies are excluded unless a complete remission was achieved at 12 months prior to study entry and no additional therapy is required or anticipated to be required during the study period (exceptions include but are not limited to, non-melanoma skin cancers; in situ bladder cancer, in situ gastric cancer, or in situ colon cancer; in situ cervical cancer/dysplasia; or breast carcinoma in situ). 7. History of Grade ≥ 3 allergy to human monoclonal antibodies. 8. Subjects who have had prior immunotherapy, including but not limited to interferon alfa-2b, PEG-IFN, anti-PD-1, anti-PD-L1, anti-CTLA4 intra-tumoral or vaccine therapies are not permitted to enroll. 9. Psychological, familial, sociological, or geographical conditions that potentially hamper compliance with the study protocol and follow-up schedule; those conditions should be discussed with the participant before registration in the trial. 10. Subjects who are receiving any other investigational agents. 11. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection (requiring systemic therapy), symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. 12. Patients known history of positive test for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS). Note: Testing for HIV must be performed at sites where mandated locally. 13. Subjects who are unable or unwilling to discontinue use of prohibited medications. 14. Subject is a prisoner 15. Subjects that have undergone a solid organ or stem cell transplant.