Azadirachta Indica in Treating Patients With Chronic Lymphocytic Leukemia

Inclusion Criteria: * Patients must have a definitive diagnosis of CLL as defined by the IWCLL criteria * Patients may not have received any prior treatment for management of CLL; (no more than 30 patients with treatment naive disease will be included in this study) * Patients with advance stage disease (Rai Stage II-IV) may be included in this clinical trial if they refuse to take standard chemotherapeutic regimens * Patients with relapsed or relapsed/ resistant may be included in this clinical trial if they refuse to take standard chemotherapeutic regimens * Patients must understand and voluntarily sign an informed consent form * Have an ECOG Performance Status of =\< 2 at study entry * Able to adhere to the study visit schedule and other protocol requirements * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Hemoglobin \>= 10g/dl * Platelets \>= 50,000/mcl * Total bilirubin within normal institutional limits * AST (SGOT)/ ALT (SGPT) =\< 2.5 X institutional ULN * Patients of childbearing potential must agree to use acceptable contraceptive methods (e.g., double barrier) during treatment * Patient or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure Exclusion Criteria: * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form * Any condition, including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study * Trying to conceive, pregnant or breast feeding female patients * Unwilling or unable to follow protocol requirements * Any condition which in the Investigator's opinion deems the patient an unsuitable candidate to receive study drug * Patients who are consuming other herbals or non-traditional therapies (i.e. green tea extracts and cumin) within the last 4 weeks(28 days) of initiating this clinical study; note: patient must have stopped herbal or other non-traditional therapies for CLL at least 28 days prior to initiating therapy on this study * Patients with high-risk cytogenetic (del 17p, del 11q) determined by FISH analysis * Prior organ transplant