Inclusion Criteria:

* Patients must be ≥ 18 years of age
* Histologically confirmed classical HCL by the enrolling institution
* Presence of BRAF V600E mutation as confirmed by PCR, NGS or immunohistochemistry. If patient is known to have negative BRAF mutation, repeat testing is advisable as well as discussion with the main study principal investigator.
* Has not received any prior therapy for the disease
* 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 and cladribine, and 18 months after discontinuation of rituximab and obinutuzumab
* 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 women of childbearing potential

Exclusion Criteria:

* Have had previous treatment for HCL, including purine analogs, vemurafenib, rituximab, obinutuzumab, and other investigational agents. Previous treatment with transfusions and other supportive care such as G-CSF and erythropoietin are allowed.
* Known hypersensitivity to any of the study drugs.
* Patients with known long QT syndrome or uncorrectable electrolyte abnormalities
* Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis.
* Presence of positive test results for hepatitis B virus (HBV), hepatitis B surface antigen (HBsAg) or hepatitis C (HCV) antibody

° Patients with occult or prior HBV infection (defined as positive total hepatitis B core antibody \[HBcAb\] and negative HBsAg) may be included if HBV DNA is undetectable. These patients must be willing to undergo monthly DNA testing and take HBV viral prophylaxis such as entecavir.
* Known infection with HIV or human T-cell leukemia virus 1 (HTLV-1)
* Active uncontrolled infection, e.g. persistent bacteremia, supplemental oxygen or pressor supports, etc.
* Live vaccination within 28 days of randomization
* Patients with concurrent active malignancies as defined by malignancies requiring any therapy other than expectant observation or hormonal therapy, with the exception of squamous and basal cell carcinoma of the skin, in situ cervical cancer, adequately treated stage I/II cancer from which the patient is current in complete remission, or any other cancer from which the patient has been disease free for five years
* Malabsorption syndrome or other condition that precludes enteral route of administration
* Patients with HCL variant (as defined by absence of expression of CD25)
* Pregnant or lactating, or intending to become pregnant during the study