PRE-REGISTRATION (STEP 0)

All patients are REQUIRED to be pre-registered to A041202 in order to submit peripheral blood to the Alliance Hematologic Malignancy Biorepository (HEME) for central Zap-70 methylation. This specimen submission is mandatory prior to registration as results will be used for stratification

REGISTRATION (STEP 1)

Patients must be diagnosed with CLL in accordance with International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria that includes all of the following:

\>= 5 x 10\^9 B lymphocytes (5000/uL) in the peripheral blood

On morphologic review, the leukemic cells must be small mature lymphocytes, and prolymphocytes must not exceed 55% of the blood lymphocytes

CLL cells on immunophenotype (performed locally) must reveal a clonal B-cell population, which express the B cell surface markers of CD19 and CD20, as well as the T-cell antigen CD5; patients with bright surface immunoglobulin expression or lack of CD23 expression in \> 10% of cells must lack t(11;14) translocation by interphase cytogenetics

Patients must be intermediate or high-risk Rai stage CLL

Intermediate risk (formerly Rai stage I/II) is defined by lymphocytosis plus enlarged lymph nodes at any site, with or without hepatomegaly or splenomegaly

High risk (formerly Rai stage III/IV) is defined by lymphocytosis with or without enlarged nodes and spleen plus disease-related anemia (hemoglobin \< 11 g/dL) or thrombocytopenia (platelet count \< 100 x 10\^9/L) that is not attributable to autoimmune hemolytic anemia or thrombocytopenia

Patients must meet criteria for treatment as defined by IWCLL 2008 guidelines which includes at least one of the following criteria:

Evidence of marrow failure as manifested by the development or worsening of anemia or thrombocytopenia (not attributable to autoimmune hemolytic anemia or thrombocytopenia)

Massive (\>= 6 cm below the costal margin), progressive or symptomatic splenomegaly

Massive nodes (\>= 10 cm) or progressive or symptomatic lymphadenopathy

Autoimmune anemia and/or thrombocytopenia that is poorly responsive to standard therapy

Constitutional symptoms, which include any of the following:

Unintentional weight loss of 10% or more within 6 months

Significant fatigue

Fevers \> 100.5 degrees F for 2 weeks or more without evidence of infection

Night sweats \> 1 month without evidence of infection

Age \>= 65 years

Eastern Cooperative Oncology Group (ECOG) performance status 0-2

Patients with active hepatitis B defined by hepatitis B surface antigen positivity or core antibody positivity in the presence of hepatitis B DNA are not eligible for this study; patients with a positive hepatitis B core antibody but with negative hepatitis B DNA may participate, but must have hepatitis serologies and hepatitis B DNA monitored periodically by the treating physician

Intravenous immunoglobulin (IVIG) can cause a false positive hepatitis B serology; if patients receiving routine IVIG have core antibody or surface antigen positivity without evidence of active viremia (negative hepatitis B DNA) they may still participate in the study, but should have hepatitis serologies and hepatitis B DNA monitored periodically by the treating physician

Patients with class III or class IV heart failure by New York Heart Association, those with unstable angina, and those with uncontrolled arrhythmia are not eligible

Patients who have had a myocardial infarction, intracranial bleed, or stroke within the past 6 months are not eligible

Patients with known human immunodeficiency virus (HIV) are eligible if their CD4 count is \>= 350 cells/mm\^3 and if they are not taking prohibited CYP-interacting medications

Patients may not have had major surgery within 10 days of enrollment, or minor surgery within 7 days of enrollment; examples of minor surgery include dental surgery, insertion of a venous access device, skin biopsy, or aspiration of a joint; the decision about whether a surgery is major or minor can be made at the discretion of the treating physician

Absolute neutrophil count (ANC) \>= 1,000/uL unless due to bone marrow involvement

Aspartate aminotransferase (AST) or alanine aminotransferase (AST) =\< 2.5 x upper limits of normal except if due to disease infiltration of the liver

Bilirubin =\< 1.5 x upper limits of normal (unless due to liver involvement, hemolysis, or Gilbert's disease)

Creatinine clearance \>= 40 mL/min

To be calculated by modified Cockcroft-Gault formula

Platelet count (untransfused) \>= 30,000/uL

Prior treatment

Patients must not have had prior therapy for CLL (except palliative steroids or treatment of autoimmune complications of CLL with rituximab or steroids)

Treatment with rituximab and/or high dose corticosteroids for autoimmune complications of CLL must be complete at least 4 weeks prior to enrollment; palliative steroids must be at a dose not higher than 20 mg/day of prednisone or equivalent corticosteroid at the time of registration

Patients must not be receiving active systemic anticoagulation with heparin or warfarin; patients must be off warfarin therapy for at least 30 days prior to enrollment

Patients must not have any history of Richter's transformation or prolymphocytic leukemia (prolymphocytes in blood > 55%)

Patients must not require more than 20 mg prednisone or equivalent corticosteroid daily

Patients must not have uncontrolled active systemic infection requiring intravenous antibiotics

Patients must not have continued requirement for therapy with a strong cytochrome P450 3A4/5 (CYP3A4/5) inhibitor or inducer

Patients must not have a known allergy to mannitol

Patients must not have prior significant hypersensitivity to rituximab (not including infusion reactions)

• Hematology

• Oncology (Adult)

• National Cancer Institute (NCI)