Alemtuzumab-Ofatumumab in Previously Untreated Symptomatic Chronic Lymphocytic Leukemia

Inclusion Criteria: * Patients must be Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Patients must have a confirmed diagnosis of CLL as defined by the International Workshop on CLL (iwCLL) 2008 (iwCLL2008) criteria below: * Presence of at least 5x10\^9 B lymphocytes/L (5000/uL) in the peripheral blood * Morphologically, the lymphocytes must appear of small to moderate size with \< 55% prolymphocytes, atypical lymphocytes or lymphoblasts * The clonality and immunophenotype of the circulating B-lymphocytes must be confirmed by flow cytometry to express CD5, CD23, CD19, CD20, CD52 and either kappa or lambda light chain * Patients must have symptomatic disease requiring therapy; indications for therapy are defined by the iwCLL2008 criteria as follows (one or more are sufficient): * Clinical manifestations (if believed by the investigator to be caused by CLL): a) Unintentional weight loss \> 10% within the previous 6 months; b) significant fatigue; c) fevers of greater than 100.5 degrees Fahrenheit (F) (38 degrees Celsius \[C\]) for 2 weeks without evidence of infection; d) night sweats without evidence of infection * Evidence of progressive marrow failure as manifested by the development or worsening of anemia (\< 11 g/dl), thrombocytopenia (\< 100,000/mm\^3) or neutropenia (\< 1,500/mm\^3) * Massive (i.e. \> 6 cm below left costal margin) or progressive splenomegaly * Massive nodes/clusters (\> 5 cm) or progressive symptomatic adenopathy * Progressive lymphocytosis with an increase of \> 50% over 2 month period, or an anticipated doubling time of less than 6 months * NOTE: Marked hypogammaglobulinemia or the development of a monoclonal protein in the absence of any of the above criteria for active disease is not sufficient for protocol therapy * Patients must have evidence of adequate bone marrow reserve as shown by absolute neutrophil count (ANC) of at least 1,000/mm\^3; however, if the cytopenias are due to extensive bone marrow involvement by CLL, patients may be included in the study * And patients must have evidence of adequate bone marrow reserve as shown by platelet count of at least 50,000/mm\^3; however, if the cytopenias are due to extensive bone marrow involvement by CLL, patients may be included in the study * Serum creatinine must be less than 2.0 mg/dl obtained within 2 weeks prior to study enrollment; if serum creatinine is greater than 1.5 mg/dl, the creatinine clearance calculated from a 24 hour urine collection must be greater than 40 ml/min * Total bilirubin must be less than 2 mg/dl (unless due to CLL involvement of liver or a known history of Gilbert's disease) * Aspartate aminotransferase (AST), alanine aminotransferase (ALT) must be no more than 2.5 times upper limit of normal unless due to disease involvement of the liver * Alkaline phosphatase must be no more than 2.5 times upper limit of normal unless due to disease involvement of the liver * All patients must have given a signed, informed consent prior to enrollment on study Exclusion Criteria: * Prior cytotoxic therapies are NOT allowed; the only exception is prior corticosteroid therapy (prednisone up to 1 mg/kg for =\< 3 months) which must be stopped at least 1 week prior to study enrollment * Patients with active autoimmune anemia or autoimmune thrombocytopenia are NOT eligible * Patients who have current active hepatic or biliary disease (with the exception of patients with Gilbert's syndrome, asymptomatic gallstones, liver involvement by CLL, or stable chronic liver disease per investigator assessment) are NOT eligible * Patients with active chronic or current infections requiring oral or intravenous antibiotics are NOT eligible for enrollment to the study until resolution of the infection and completion of therapeutic antibiotics * Patients with a past or current second malignancy are NOT eligible aside from the following exceptions: * Patients who have been free of malignancy for at least 5 years * Patients who have a history of completely resected basal or squamous cell skin cancer, successfully treated in situ carcinoma of the breast or cervix, or pre-cancerous lesions of the colon * Patients with known human immunodeficiency virus (HIV) are NOT eligible for the study * Patients with history of significant cerebrovascular disease in the past 6 months or ongoing event with active symptoms or sequelae are NOT eligible for the study * Patients with clinically significant cardiac disease including unstable angina, acute myocardial infarction within six months prior to enrollment, congestive heart failure (New York Heart Association \[NYHA \] III-IV), and arrhythmia unless controlled by therapy (with the exception of extra systoles or minor conduction abnormalities), are NOT eligible * Patients with significant concurrent, uncontrolled medical condition including, but not limited to, cardiovascular, renal, hepatic, gastrointestinal, endocrine, pulmonary, neurological, cerebral or psychiatric disease which in the opinion of the investigator may represent a risk for the patient, are NOT eligible * Patients with positive serology for Hepatitis B (HB), defined as a positive test for HB surface antigen (HBsAg), are NOT eligible; if negative for HBsAg but HB core antibody (HBcAb) positive a HB deoxyribonucleic acid (DNA) test will be performed; if HB DNA test is positive the patient is NOT eligible; NOTE: patients who are positive for HBcAb but negative for hepatitis B virus (HBV) antigenemia and viremia (HBsAg negative and HB DNA test negative) may be eligible for the study, but must be started on HBV suppression therapy with lamivudine or equivalent anti-HBV agents throughout the treatment and for a year after the completion of the treatments; these patients need to have liver function tests (LFTs) and HBV viral titer monitoring at least monthly during the treatment and for a year after treatment completion * Patients with positive serology for hepatitis C are NOT eligible * Women of childbearing potential and sexually active males must commit to the use of adequate contraception from the study start to one year after the last dose of study treatment * Childbearing potential is defined as any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy; or * Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months) * Adequate contraception is defined as hormonal birth control, intrauterine device, barrier method or total abstinence; patients who are unable or unwilling to use adequate contraception are NOT eligible * Women who are pregnant or lactating are NOT eligible