The purpose of this study is to evaluate pharmacodynamic changes of BMS-936559 treatment on the biomarkers measured in the peripheral blood and tumor tissues of subjects with unresectable Stage III or IV Melanoma.

Inclusion Criteria:

• Men and women ≥ 18 years
• Eastern Cooperative Oncology Group (ECOG) status = 0 to 1
• Subjects with unresectable Stage III or IV Melanoma who are either refractory or intolerant to, or have refused standard therapy for treatment of metastatic Melanoma
• Subject must have histologic or cytologic confirmation of advanced Melanoma
• Subjects must have at least one measurable lesion at baseline by computed tomography (CT) or magnetic resonance imaging (MRI) as per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria
• Subjects must have at least 1 tumor site that can be biopsied at acceptable clinical risk and must consent to pre- and post-treatment biopsies

Exclusion Criteria:

• Active or progressing brain metastases
• Other concomitant malignancies (with some exceptions per protocol)
• Active or history of autoimmune disease
• Positive test for human immunodeficiency virus (HIV) 1&2 or known acquired immunodeficiency syndrome (AIDS)
• History of any hepatitis
• Prior therapy with any antibody/drug that targets the T cell coregulatory proteins, including but not limited to, anti Programmed cell death 1 (PD-1), anti Programmed cell death ligand 1 (anti-PD-L1), anti-PD-L2, anti-CD137, anti-OX-40, anti-CD40 or anti Cytotoxic T lymphocyte-associated antigen 4 (anti-CTLA-4) antibodies