Inclusion Criteria:

          -  ≥ 18 years of age

          -  Histologically confirmed classical HCL with one of the following:

          -  Intolerance to purine analogs or considered to be poor candidates for purine
             analog-based therapy

          -  Failure to achieve any response (CR or PR) to the initial purine analog-based therapy

          -  Relapse ≤ 2 years of purine analog-based therapy

          -  ≥ 2 relapses Histologic confirmation of diagnosis will be performed at MSKCC or a
             participating site.

          -  Patients who meet the standard treatment initiation criteria, as defined by ANC ≤1.0,
             Hgb ≤ 10.0 or PLT ≤100K

          -  ECOG performance status of 0-2

          -  Acceptable pre-study organ function during screening as defined as: Total bilirubin ≤
             1.5 times the upper limit of normal (ULN), aspartate aminotransferase (AST) and
             alanine aminotransferase (ALT) ≤ 2.5x ULN, and serum creatinine ≤ 1.5x ULN

          -  Electrocardiogram (ECG) without evidence of clinically significant ventricular
             arrhythmias or ischemia as determined by the investigator and a rate-corrected QT
             interval (QTc, Bazett's formula) of < 480 msec.

          -  For women of childbearing potential, agreement to the use of two acceptable methods of
             contraception, including one barrier method, during the study and for 6 months after
             discontinuation of vemurafenib

          -  For men with female partners of childbearing potential, agreement to use a latex
             condom and to advise their female partner to use an additional method of contraception
             during the study and for 6 months after discontinuation of vemurafenib

          -  Negative serum pregnancy test within 7 days of commencement of treatment in
             premenopausal women.

          -  Agreement not to donate blood or blood products during the study and for at least 6
             months after discontinuation of vemurafenib; for male partners, agreement not to
             donate sperm during the study and for at least 6 months after discontinuation of
             vemurafenib

          -  Ability to understand and willingness to sign a written informed consent document.

          -  Willingness and ability to comply with scheduled visits, treatment plans, laboratory
             tests, and other study procedures.

        Exclusion Criteria:

          -  Pregnant or breast-feeding

          -  Have had chemotherapy (including purine analogs, rituximab, and other investigational
             agents) within six weeks prior to entering the study

          -  Major surgery within 4 weeks prior to entering the study

          -  Invasive malignancy within the past 2 years prior to first study drug administration,
             except for adequately treated (with curative intent) basal or squamous cell carcinoma,
             melanoma, in situ carcinoma of the cervix, in situ ductal adenocarcinoma of the
             breast, in situ prostate cancer, or limited stage bladder cancer or other cancers from
             which the patient has been disease-free for at least 2 years

          -  Refractory nausea or vomiting, malabsorption, external biliary shunt, or history of
             any type of gastrointestinal surgery that would preclude adequate absorption of study
             drug

          -  Prior treatment with MEK or BRAF inhibitors

          -  Active HIV, hepatitis B and hepatitis C

          -  Patients with HCL variant (as defined by absence of expression of CD25 or absence of
             BRAF V600E mutation)