The purpose of this study is to see if the combination of entinostat and pembrolizumab can be an effective treatment for patients with melanoma of the eye (uveal melanoma) that has spread to other sites of the body (metastatic disease). Pembrolizumab is an antibody that helps the immune system to attack cancer cells. Although pembrolizumab has proven clinical efficacy in treating patients with metastatic cutaneous melanoma, an effect on metastatic uveal melanoma has not been established. Entinostat is a histone deacetylase (HDAC) inhibitor that has effects on both cancer cells and immune regulatory cells, thus potentially enhancing the effects of immunotherapy.

Inclusion Criteria:

• Age above 18 years.
• Signed and dated written informed consent before the start of specific protocol procedures.
• ECOG PS 0-1
• Histologically/cytologically confirmed stage IV uveal melanoma
• Measurable disease by computed tomography (CT) or Magnetic Resonance Imaging (MRI) per RECIST 1.1 criteria
• Any number of prior therapies (including none), with the exception of anticancer immunotherapy

Exclusion Criteria:

• Active brain metastases (symptomatic and/or requiring corticosteroids) or leptomeningeal metastases
• Previous treatment with anticancer immunotherapy
• Pregnant or nursing (lactating) women
• Medical, psychiatric, cognitive or other conditions that may compromise the patient's ability to understand the patient information, give informed consent, comply with the study protocol or complete the study
• Active autoimmune disease
• Immune deficiency or treatment with systemic corticosteroids
• Use of other investigational drugs (drugs not marketed for any indication) within 28 days before study drug administration
• Life expectancy of less than 3 months