The Primary hypothesis of this study is that because of its effect as a potent immunosuppressive agent targeting lymphocytes, pentostatin will show a sustained response in pediatric subjects with severe chronic GVHD. Secondary hypotheses include that the infection and toxicity rate of pentostatin in this setting will be acceptable given its lack of severe myelosuppression, and subjects with refractory chronic GVHD will have significant QOL impairment and symptomatology. These may change as subjects are being treated for their chronic GVHD with pentostatin.