- Have new onset of moderate or severe cGvHD as assessed by the NIH Consensus Criteria Clinical Assessment (staging and severity) with onset within 2 years of transplantation (Patients with prior acute GvHD should be on a stable dose of <0.5 mg/kg daily prednisone, or equivalent, for at least 2 weeks prior to study entry. Prior ECP for patients with acute GvHD is permitted in the study);willing to start 1.0mg/kg prednisone: Be using adequate birth control; If a woman, must have negative pregnancy test result at screening: Be able and willing to comply with all study procedures including providing informed consent