Adjuvant Nivolumab & Low Dose Ipilimumab for Stage III & Resected Stage IV Melanoma

Inclusion Criteria: * Histologically or cytologically proven melanoma. The primary site of melanoma may be cutaneous on other body site such as ocular or anorectal. Documentation required to be sent to BrUOG. * Completely resected stage III (lymph node positive) or resected stage IV disease. Patients with stage T4BN0 are also eligible. It is required that patients with stage IIIA disease have \> 1mm nodal involvement via pathology assessment of the resected node. All patients must be disease free to be eligible. * No prior treatment for melanoma other than surgical resection or radiation. At least 4 weeks since prior surgery and 3 weeks since prior radiation to registration date. * Age \>/= 18 years * ECOG performance status 0-1 * Patients must have organ and marrow function as defined below within 14 days of study entry: Hematologic Absolute neutrophil count (ANC) \>/= 1.5 X 109/L; Hemoglobin \>/= 9.5 g/dL; Platelets \>/= 100 X 109/L; Total Bilirubin ≤ 1.5 x ULN except subjects with normal direct bilirubin or those with known Gilbert's syndrome. Send information to BrUOG if patient has known Gilbert's syndrome AST and ALT \</= 2.5 X ULN Albumin \>/= 2.5 g/dL Renal Creatinine OR Calculated creatinine clearance : Creatinine \</= 1.5 mg/dl or creatinine clearance \> 50ml/min * No clinically significant coagulation disorder as defined by the treating MD. Therapeutic use of anticoagulants is permissible. Add to concomitant medication log if applicable. * Not pregnant and not nursing. Women of child bearing potential must have a negative serum pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 7 days prior to Day 1 of treatment. Post-menopausal women (surgical menopause or lack of menses \>12 months) do not need to have a pregnancy test, please document status. * Confirmation of informed consent. * Men and women of childbearing potential enrolled in this study must agree to use adequate barrier birth control measures during the course of the study and up to 2 months after end of treatment. Exclusion Criteria: * Currently receiving cancer therapy (chemotherapy, radiation therapy, immunotherapy, or biologic therapy) or investigational anti-cancer drug * Brain metastases, whether resected or not, and any known leptomeningeal disease or known bone metastases. * Pregnant or breastfeeding female * Unwillingness or inability to follow the procedures required in the protocol, to document * Any serious or uncontrolled medical disorder that, in the opinion of the investigator, may increase the risk associated with study participation or study drug administration, impair the ability of the subject to receive protocol therapy, or interfere with the interpretation of study results. * Prior malignancy active within the previous 2 years except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the prostate, cervix, or breast. Documentation required to be sent to BrUOG * Subjects with active, known or suspected autoimmune disease. Subjects with vitiligo, controlled type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. * Subjects with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \>10mg daily of prednisone equivalents are permitted in the absence of active autoimmune disease. * Prior treatment with an anti-PD-1, anti-PD-L1 or anti-CTLA-4 antibody * Any positive test result for hepatitis B or C virus indicating acute or chronic infection * Known history of testing positive for human immunodeficiency virus or known acquired immunodeficiency syndrome * History of severe hypersensitivity reaction to any monoclonal antibody. * Patients with unstable angina (anginal symptoms at rest) or new-onset angina (began within the last 3 months) or myocardial infarction within the past 6 months. * History of autologous transplant or organ allograft even if not taking immunosuppressive medications