Inclusion Criteria:

          -  For Phase I: Locally advanced or metastatic BRAF V600E/K/R positive melanoma that is
             either treatment-naïve or treatment-experienced. For the latter, progression, or
             stable as best response, or intolerance to the last treatment is required. Previous
             treatments can be local or systemic therapies. There are no limits to the number of
             prior therapies. For all patients, disease does not have to be measurable but must be
             evaluable, which is defined as one or more lesions which are known to be present, but
             which cannot be measured. eg: Bony lesions, pleural effusion, ascites.

          -  For Phase I: For treatment-experienced patients, the following washout periods are
             required prior to enrollment on the study: 2 weeks wash out after prior local therapy
             (such as radiation therapy or intra-lesional therapy), 4 weeks wash out after
             cytotoxic therapy or high dose interleukin-2, and 6 weeks wash out after anti-PD-1 or
             anti-PD-L1 therapy. For all other therapy not mentioned, a wash out period of at least
             5 half lives will be needed.

          -  For phase II: Histological diagnosis of BRAF V600E/K melanoma, unresectable stage III
             or stage IV, according to the AJCC Staging Manual, 7th Edition, 2011. Must have
             measurable disease, and no prior systemic treatment for locally advanced or metastatic
             melanoma. Previous local therapy is allowed. Previous systemic treatment for any stage
             III disease that was subsequently rendered NED (no evidence of disease) by surgery is
             allowed except for ipilimumab and BRAF inhibitors. Patients with resectable disease
             who do not want surgery for any reason are also allowed. Measurable disease is defined
             as least one lesion that can be accurately measured in two dimensions with both
             diameters greater than 1.0cm. For CT/MRI evaluations, an effective slice thickness is
             required of less than or equal to 5 mm. For slice thickness greater than 5mm, both
             diameters must be greater than or equal to 2.0cm at baseline.

          -  ECOG performance status 0, 1 or 2

          -  Negative pregnancy test for women of childbearing potential within 7 days of starting
             study treatment.

          -  Lab testing results in accordance with protocol WBC greater/equal to 2,000/mm3 ANC
             greater/equal to 1200/mm3 Platelet greater/equal 1000,000/mm2 Hemoglobin greater/equal
             9 gm/dL (may be transfused) Serum bilirubin levels less/equal 1.5 mg/dL except for
             patients with Gilbert's syndrome.

          -  Serum aspartate transaminase (AST) and serum alanine transaminase (ALT) less/equal 2.5
             X upper limit of normal Alkaline phosphatase less/equal 2.5 times upper limit of
             normal Serum Creatinine levels less/equal 1.5 mg/dL Left Ventricular Ejection Fraction
             (LVEF) greater or equal to lower limit of normal by ECHO Women of childbearing
             potential should be advised to avoid becoming pregnant and men should be advised to
             not father a child while receiving treatment with ipilimumab or dabrafenib. Patients
             should agree to use an appropriate method of birth control while on study.

          -  Age greater than 18 years and of any gender or race. Able to provide informed consent
             and have signed an approved consent form that conforms to federal and institutional
             guidelines.

        Exclusion Criteria:

          -  Concurrent therapy with any other non-protocol anti-cancer therapy

          -  Prior systemic treatments with either ipilimumab or a BRAF inhibitor (such as
             vemurafenib or dabrafenib).

          -  Prior local therapy within 2 weeks (for both phases I and II) or prior systemic
             therapy within 4 weeks of starting protocol treatment (phase I).

          -  For phase II: Any prior systemic therapy for locally advanced or metastatic melanoma.
             Prior local therapy such as radiation or intratumoral injection is allowed. Previous
             systemic treatment for any stage III disease that was subsequently rendered NED (no
             evidence of disease) by surgery is allowed.

          -  Brain metastases (except if all known lesions were previously treated with surgery or
             stereotactic radiosurgery and lesions, if still present, are confirmed stable for
             greater than or equal to 2 weeks prior to enrollment, and are asymptomatic with no
             corticosteroid requirements for greater than or equal to weeks prior to randomization,
             and no enzyme inducing anticonvulsants for greater than or equal to 2 weeks prior to
             randomization). Brain MRI or CT is required at screening.

          -  Anyone with a second malignancy expected to require cytotoxic chemotherapy or immune
             modulating therapy within 3 months of enrollment

          -  Pre-existing autoimmunity: History of inflammatory bowel disease; history of
             symptomatic autoimmune disease (e.g., rheumatoid arthritis, systemic progressive
             sclerosis [scleroderma], systemic lupus erythematosus, autoimmune vasculitis [e.g.,
             Wegener's Granulomatosis]); motor neuropathy considered of autoimmune origin (e.g.,
             Guillain-Barre Syndrome). Subjects with vitiligo, 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.

          -  No concurrent systemic corticosteroids (or other systemic immunosuppressant's),
             including oral steroids (i.e. prednisone, dexamethasone), continuous use of topical
             steroid creams or ointments, or ophthalmologic steroids. If a subject is currently
             taking corticosteroids, treatment should be discontinued two weeks prior to starting
             protocol therapy. Occasional use of steroid inhalers is allowed.

          -  Any serious or uncontrolled medical disorder or active infection that, in the opinion
             of the investigator, may increase the risk associated with study participation, study
             drug administration, or would impair the ability of the subject to receive protocol
             therapy.

          -  Any known positive test for hepatitis B virus or hepatitis C virus indicating acute or
             chronic infection. Known history of testing positive for human immunodeficiency virus
             (HIV) or known acquired immunodeficiency syndrome (AIDS).

          -  Herbal remedies (e.g., St. John's wort) within 1 week of enrollment.

          -  Drugs that are strong inhibitors or inducers of CYP3A or CYP2C8, p-glycoprotein (Pgp)
             or Bcrp transporter because they may alter dabrafenib concentrations. The list may be
             modified based on emerging data; consider therapeutic substitutions for these
             medications. Patients must be off treatment for at least 1 week prior to enrollment.

          -  A history of known glucose-6-phosphate dehydrogenase (G6PD) deficiency.

          -  The presence of any other medical or psychiatric disorder that, in the opinion of the
             treating physician, would contraindicate the use of the drugs in this protocol or
             place the subject at undue risk for treatment complications

          -  Pregnancy or breast feeding

          -  A history of a severe hypersensitivity reaction to ipilimumab or dabrafenib

          -  Any reason why, in the opinion of the investigator, the patient should not participate