Phase II Maraviroc for GVHD Prevention

Inclusion Criteria: * Patients ≥18 years of age with a hematologic malignancy other than aplastic anemia or primary myelofibrosis, scheduled to undergo RIC allogeneic SCT with a peripheral blood stem cell graft from an unrelated donor, using Flu/Bu conditioning and Tac/MTX GVHD prophylaxis. The following diagnoses are included: * Acute leukemia - AML, ALL or acute biphenotypic leukemia. Patients will have documentation of complete remission within 6 weeks prior to their transplant. Complete remission is defined as \<5% blasts on a bone marrow biopsy and absence of any known extramedullary disease. * Chronic myelogenous leukemia in any stage, but with documentation of \<5% blasts on a bone marrow biopsy within 6 weeks prior to transplant. * Myelodysplastic syndrome of any subtype, but with documentation of \<5% blasts on a bone marrow biopsy within 6 weeks prior to transplant. * Myeloproliferative disorders other than primary myelofibrosis. * Lymphoma - All types of lymphoma are eligible. * CLL and PLL. * Patients who meet institutional eligibility criteria for allogeneic SCT: * Renal function: Serum creatinine ≤2. * Hepatic function: Baseline direct bilirubin, ALT or AST lower than three times the upper limit of normal. * Pulmonary disease: FVC or FEV1 ≥ 40% predicted. * Cardiac ejection fraction ≥ 40%. * Availability of an unrelated donor, identified and screened by the NMDP. The donor will have at least 7/8 HLA-A, -B, -C and -DRB1 matching by high resolution molecular typing and will meet NMDP eligibility criteria to serve as a peripheral blood stem-cell donor. * Karnofsky score ≥ 70% at the time of screening. * Capacity to understand and sign the study informed consent form. * Negative pregnancy test. Women of childbearing potential (not having had a hysterectomy, a bilateral oophorectomy or bilateral tubal ligation, or be post-menopausal with a total cessation of menses of \> 1 year) must agree to use documented reliable method(s) of contraception. Men should agree to use condoms during the study period. * Co-enrollment in other clinical trials that do not include experimental GVHD therapies is allowed. Exclusion Criteria * Patients with aplastic anemia or primary myelofibrosis. Patients with marrow fibrosis secondary to MDS, AML or a myeloproliferative disorder other than primary myelofibrosis are eligible. * Patients who are not expected to be available for follow-up in our institution for at least 180 days after the transplant. * Prior allogeneic SCT. * Uncontrolled bacterial, viral or fungal infections. * Patients who receive maraviroc for the treatment of HIV infection. * Patients receiving other investigational drugs for GVHD. * Co-enrollment in other clinical trials that do not include experimental GVHD therapies is allowed. * Patients with prior malignancies are excluded unless treated with curative intent and known to be free of disease for at least 2 years.