Background: Chronic GVHD is a medical condition that can become very serious. Chronic GVHD is a common development after allogeneic transplant that occurs when the donor cells attack and damage tissues. The primary purpose of this study is to compare treatment regimens that contain sirolimus without a calcineurin inhibitor to a comparator regimen of sirolimus with a calcineurin inhibitor and evaluate how well chronic GVHD responds to treatment. The combinations of medications in this study are: