Inclusion Criteria: A. Common to All Indications: - Life expectancy at least 12 weeks - ECOG Performance Status of 0-2 B. For Follicular Lymphoma (FL), Diffuse Large B-Cell Lymphoma (DLBCL) Subjects: - Must be at least 4 weeks (for FL) or 2 weeks (for DLBCL) since prior cytotoxic, biologic, monoclonal antibody, or investigational therapy - Ability to undergo tumor biopsy pre-treatment and at end of monotherapy period (though not mandatory for all subjects) - Subjects must have a histologically confirmed diagnosis of relapsed or refractory disease C. For Chronic lymphocytic leukemia (CLL) Subjects: - Subjects must have a histologically confirmed diagnosis of relapsed or refractory disease - Must be at least 4 weeks since prior cytotoxic, biologic, monoclonal antibody, or investigational therapy, including corticosteroids Exclusion Criteria: A. Common to All indications: - Prior anti-CXCR4 therapy including BMS-936564 (MDX-1338) - Less than 3 months from prior hematopoietic stem cell transplant - Presence of active graft versus host disease B. For FL, DLBCL Subjects: - (For DLBCL): Inadequate renal function defined as creatinine clearance (by Cockcroft-Gault formula) < 60 mL/min - Major surgery, not related to debulking procedures, within 21 days of first dose - Myocardial infarction within 6 months prior to screening or Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia - Myelodysplastic syndrome (MDS) C. For CLL Subjects: - No progression to more aggressive B-cell cancers, such as Richter's syndrome - Major surgery within 21 days of Cycle 1, Day 1. Patients undergoing debulking procedures and minor surgery are allowed after a recovery period, in the judgment of the Investigator - Myocardial infarction within 6 months prior to screening Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia