A Study of Nivolumab and Hydroxychloroquine or Nivolumab/Ipilimumab and Hydroxychloroquine in Advanced Melanoma

Inclusion Criteria: * Histological or cytological evidence of melanoma, unresectable Stage III or Stage IV, any genotype, and any programmed death-ligand 1 (PD-L1) immunohistochemistry (IHC) status * Phase 1a: nivolumab + HCQ: any prior treatment, or treatment naïve * Phase 2: nivolumab + HCQ: * \- - Cohort 2a: prior immunotherapy in the adjuvant or metastatic setting is required * \- - Cohort 2b: anti-PD-1 Ab-naïve, but may have received any prior other therapy * Phase 1b nivolumab + ipilimumab + HCQ: anti-PD-1 refractory * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * At least one measurable site of disease by RECIST 1.1 criteria that has not been previously irradiated. * Fresh or archived primary or metastatic tissue available for submission for correlative analyses * Negative serum pregnancy test within 28 days prior to commencement of dosing in premenopausal women. Negative urine pregnancy test within 24 hours of starting treatment. * Able to swallow and retain oral medication and no clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels * Adequate baseline organ function Exclusion Criteria: * Known serious concurrent infection or medical illness, including psychiatric disorders, which would jeopardize the ability to receive the protocol treatment with reasonable safety. * Pregnant or breast-feeding. * Patients with brain metastases treated with whole brain radiation that have been stable for 2 months are eligible; patients with brain metastases treated with gamma knife or surgery are allowed to participate after 2 weeks have elapsed since their procedure. Subjects are excluded if they have leptomeningeal disease or metastases causing spinal cord compression that are symptomatic or untreated or not stable for greater than or equal to 3 months (documented by imaging) or requiring corticosteroids greater than 20 mg prednisone equivalent daily. * Must have discontinued active immunotherapy, chemotherapy, or investigational anticancer therapy at least 4 weeks prior to entering the study and oral targeted therapy at least 2 weeks prior to entering the study. * All prior anti-cancer treatment-related toxicities (except alopecia and laboratory values listed in protocol eligibility) must be less than or equal to Grade 1 or irreversible (hypophysitis) according to the Common Terminology Criteria for Adverse Events version 5 at the time of starting treatment. Patients that are asymptomatic on low dose maintenance hormone replacement delivered at a stable dose for prior toxicities are eligible. * Prior or concurrent cancer therapy. Active immunotherapy, chemotherapy, or investigational anticancer therapy within 4 weeks prior to entering the study or oral targeted therapy within 2 weeks prior to entering the study * Phase 2 nivolumab + HCQ Cohort B: No prior immunotherapy is permitted * Patients known to be experiencing an objective partial response to immunotherapy at the time of study enrollment. * History of malignancy other than disease under study within 3 years of study enrollment EXCEPT: history of completely resected non-melanoma skin cancer, or history of indolent second malignancies are eligible. * Diagnosis of severe autoimmune disease requiring immunosuppressive medications. Patients with adrenal insufficiency on replacement dose steroids are eligible. * History of interstitial lung disease or chronic pneumonitis unrelated to prior immunotherapy. Prior interstitial pneumonitis related to immunotherapy that was completely treated with no need for ongoing clinical management is allowed. * Due to risk of disease exacerbation patients with porphyria or psoriasis are ineligible unless the disease is well controlled and they are under the care of a specialist for the disorder who agrees to monitor the patient for exacerbations. * Known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to study drug, or excipients or to dimethyl sulfoxide. * Patients receiving cytochrome P450 enzyme-inducing anticonvulsant drugs (i.e. phenytoin, carbamazepine, Phenobarbital, primidone or oxcarbazepine) within 4 weeks of the start of the study treatment * Current use of a prohibited medication as described in section on Potential for Drug-Drug Interaction. * History or evidence of increased cardiovascular risk