Thalidomide in Treating Patients With Relapsed Chronic Lymphocytic Leukemia

Inclusion Criteria: * Diagnosis of chronic lymphocytic leukemia (CLL) evidenced by monoclonal population of mature CD5+, CD19+, CD23+, and B cells * Relapsed after prior treatment for CLL * Active disease with 1 or more of the following characteristics: * At least 10% weight loss within the past 6 months * Fever greater than 100.5 degrees F for at least 2 weeks without evidence of infection * Night sweats without evidence of infection * Evidence of progressive marrow failure with anemia (hemoglobin less than 11 g/dL) and/or thrombocytopenia (platelet count less than 100,000/mm\^3) (i.e., any stage III or IV disease) * Autoimmune anemia and/or thrombocytopenia poorly responsive to corticosteroid therapy * Massive or progressive splenomegaly (i.e., greater than 6 cm below the left costal margin or more than 50% increase over 2 months) * Progressive lymphadenopathy (i.e., more than 50% increase over 2 months) * Progressive lymphocytosis (not due to corticosteroids) with an increase of more than 50% over a 2-month period or an anticipated doubling time of less than 6 months * Marked hypogammaglobulinemia or the development of a monoclonal protein in the absence of any of the above criteria for active disease are not considered evidence of active disease * Measurable disease * Absolute lymphocyte count greater than 5,000/mm\^3 * No bulky lymph node disease greater than 10 cm in at least 1 dimension except splenomegaly * Performance status - ECOG 0-2 * Absolute neutrophil count at least 500/mm\^3 * Platelet count at least 20,000/mm\^3 (in absence of sargramostim \[GM-CSF\]) * Hemoglobin at least 8 g/dL * Bilirubin no greater than 2.5 times upper limit of normal (ULN) * AST no greater than 2.5 times ULN * Creatinine no greater than 1.5 mg/dL * Creatinine clearance at least 60 mL/min * No other active malignancy * No peripheral neuropathy (sensory) grade 2 or greater * No active infection * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use 1 highly effective method of contraception AND 1 additional effective method of contraception for at least 4 weeks before, during, and for 4 weeks after study completion * No prior allogeneic bone marrow transplantation * At least 10 days since prior filgrastim (G-CSF) or GM-CSF * No more than 3 prior chemotherapy regimens * At least 30 days since prior chemotherapy * No concurrent corticosteroids except for adrenal insufficiency