Eligible patients will have undergone allogeneic stem cell transplantation using myeloablative or non-myeloablative conditioning regimens at least 180 days (6 months) ago. Patients must have steroid refractory chronic GVHD, defined as having persistent signs and symptoms of chronic GVHD despite the use of prednisone at >0.5 mg/kg/day or 1 mg/kg every other day for at least 4 weeks in the preceding 12 months (or equivalent dosing of alternate corticosteroids) without complete resolution of signs and symptoms. Patients with either extensive chronic GVHD or limited chronic GVHD requiring systemic therapy are eligible. Subjects must be on stable doses of immunosuppressants and corticosteroids for 4 weeks prior to enrollment, and the dose of corticosteroids must be less than 2mg/kg/day prednisone use (or equivalent). Subjects will be required to have adequate bone marrow and organ function at the time of enrollment.