The purpose of this study is to find out if an investigational drug called panobinostat can be given safely with another drug called ipilimumab. Investigators want to learn more about the side effects of this combination of drugs using different doses of panobinostat and the same dose of ipilimumab.

Inclusion Criteria:

• Men and women ≥ 18 years old
• Participants must be ipilimumab naïve with progressive unresectable Stage III or Stage IV melanoma who are either treatment naïve or may have been treated with up to 3 prior treatments for melanoma (e.g., chemotherapy, biologic or targeted therapy or IL-2).
• Histologic or cytologic confirmation of stage III or stage IV melanoma
• Measurable disease at baseline as assessed by CT and/or MRI
• Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1
• Screening laboratory values must meet the following criteria: white blood count (WBCs) ≥ 2000/μL; Neutrophils ≥ 1500/μL; Platelets ≥ 100 x 10^3/μL; Hemoglobin ≥ 9.0 g/dL; Creatinine Serum creatinine ≤ 1.5 x upper limit of normal (ULN) or creatinine clearance > 40 mL/minute (using Cockcroft/Gault formula); aspartic transaminase (AST) ≤ 3 x ULN; alanine transaminase (ALT) ≤ 3 x ULN; Total Bilirubin ≤ 1.5 x ULN (except those with Gilbert Syndrome who must have total bilirubin < 3.0 mg/dL)
• Men and women of childbearing potential (WOCBP) must be using an acceptable method of contraception to avoid pregnancy throughout the study and for at least 12 weeks after the last dose of investigational product in such a manner that the risk of pregnancy is minimized. Women must have a negative serum pregnancy test within 72 hours prior to the start of investigational product.

Exclusion Criteria:

• Known or suspected brain metastasis, or brain as the only site of disease, with the following exceptions: controlled brain metastasis (no radiographic progression at least 4 weeks following radiation and/or surgical treatment, off steroids for at least 4 weeks, and have no new or progressing neurological signs or symptoms); history of prior malignancy with the exception of carcinoma in situ of the cervix or other malignancy diagnosed > 2 years ago that has undergone potentially curative therapy with no evidence of disease for the last ≥ 2 years and that is deemed by the investigator to be at a low risk of recurrence
• Active autoimmune disease or a history of known or suspected autoimmune disease with the exception of subjects with isolated vitiligo, treated thyroiditis or resolved childhood asthma/atopy
• Known human immunodeficiency virus (HIV), active hepatitis A, or hepatitis B or C infection
• History of any hepatitis (e.g., alcohol or non-alcohol steatohepatitis (NASH), drug- related, autoimmune)
• Evidence of active infection that requires anti-bacterial, anti-viral, or anti-fungal therapy ≤ 7 days prior to initiation of study drug therapy
• History of acute diverticulitis, or current chronic diarrhea
• Active peptic ulcer disease even if asymptomatic
• History of adrenal insufficiency (including subjects using replacement therapy)
• Prior organ allograft or allogeneic bone marrow transplantation
• Uncontrolled or significant cardiovascular disease including, but not limited to, any of the following: Myocardial infarction within the past 6 months; Uncontrolled angina within the past 6 months; Any history of clinically significant ventricular arrhythmias (such as ventricular tachycardia, ventricular fibrillation or Torsades de pointes). Controlled atrial fibrillation by itself is not an exclusion criterion.; Baseline corrected QT interval (QTc) interval greater than 500 milliseconds
• Baseline toxicities from prior anti-cancer treatments > Grade 1
• Inability to be venipunctured and/or tolerate venous access
• Any major surgery within 4 weeks or a diagnostic procedure (e.g. incision, needle biopsy) within 1 day of study drug administration
• Any current or recent (within 3 months) gastrointestinal disease that could potentially impact the ability to swallow and/or absorb study drug (i.e., gastrointestinal surgery, malabsorption syndrome)
• Diabetes mellitus uncontrolled by medication
• Known drug or alcohol abuse
• Presence of underlying medical condition that in the opinion of the Investigator or Sponsor could adversely affect the ability of the subject to comply with or tolerate study procedures and/or study therapy, or confound the ability to interpret the tolerability of combined administration of panobinostat and ipilimumab in treated subjects
• History of allergy to components of ipilimumab or panobinostat, or known allergy to other antibody therapies.
• WOCBP who are unwilling or unable to use an acceptable method to minimize the risk of pregnancy for the entire study period and for at least 12 weeks after the last dose of investigational product
• Women who are pregnant or breastfeeding
• Women with a positive pregnancy test on enrollment or prior to investigational product administration
• Sexually active fertile men not using effective birth control if their partners are WOCBP
• Exposure to any investigational drug within 4 weeks of study drug administration.
• Any anti-cancer therapy (e.g., chemotherapy, biologics, radiotherapy, or hormonal treatment) within 4 weeks or at least 5 half-lives (whichever is longer) of study drug administration
• Prior therapy with an anti-CTLA4 antibody or an HDAC inhibitor
• Concurrent chemotherapy, hormonal therapy, immunotherapy regimens, or radiation therapy, standard or investigational
• Prisoners or subjects who are involuntarily incarcerated
• Subjects who are compulsorily detained for treatment of either a psychiatric or physical (e.g., infectious disease) illness

3 years, 9 months