Phase 2 Trial of Prophylactic Rituximab Therapy for Prevention of CGVHD

Recipient Inclusion Criteria: * Between 18 and 76 years of age * Chronic lymphocytic leukemia (CLL): * Unmutated IgG VH gene status * Mutated IgG VH genes (\> 2% nucleotide change compared to somatic sequence) * Complete remission benefit most from allogeneic hematopoietic stem cell transplant (HSCT). (Physicians will be encouraged to provide aggressive chemotherapy prior to nonmyeloablative transplantation.) * Mantle cell lymphoma (MCL): Transplant physicians believe subject would benefit from allogeneic HSCT. * Adequate renal (Cr \< 2.4 mg/dL) and hepatic (Bilirubin \< 3.0 mg/dL, Aspartate aminotransferase (AST) \< 100 IU) function. * Men and women of reproductive potential must agree to use an acceptable method of birth control during treatment and for six months after completion of treatment. * All subjects must provide written informed consent Donor Inclusion Criteria: * Genotypically or phenotypically human leukocyte antigen (HLA)-identical. * Age \< 76 unless cleared by institutional PI * Capable of giving written, informed consent. * Must consent to peripheral blood stem cell (PBSC) mobilization with G-CSF and apheresis Recipient Exclusion Criteria: * Recipient has a 9 of 10 or 10 of 10 HLA identical donor (high resolution molecular genotyping at HLA A, B, C and DrB1, and DQ) * Pregnancy * Lactating * Serious uncontrolled infection * HIV seropositivity * Hepatitis B or C seropositivity * Cardiac function: ejection fraction \< 40% or uncontrolled cardiac failure * Pulmonary: Diffusing capacity - carbon monoxide (DLCO) \< 50% predicted * Liver function abnormalities: elevation of bilirubin to ≥ 3 mg/dL and/or AST \> 100 * Renal: creatinine \> 2.4 * Karnofsky performance score ≤ 60% * Patients with poorly controlled hypertension (systolic blood pressure \> 150 or diastolic blood pressure \> 90 repeatedly). * Known life-threatening hypersensitivity to rituximab or other anti-B cell antibodies. * Inability to comply with the allogeneic transplant treatment. * Uncontrolled central nervous system (CNS) involvement with disease Donor Exclusion Criteria: * Identical twin to subject * Contra-indication to subcutaneous G-CSF at a dose of 16 mg/kg/d for 5 consecutive days * Serious medical or psychological illness * Prior malignancy within the preceding five years, with the exception of non-melanoma skin cancers. * HIV seropositivity