Inclusion Criteria:

   - Suitable candidates are patients with classic chronic GVHD or overlap syndrome
   (classic chronic plus acute GVHD)that is: a)Previously untreated (newly diagnosed) as
   defined by having received < 14 days of prednisone (or equivalent) before
   enrollment/randomization to study therapy; b)Previously treated but inadequately
   responding after ≤ 16 weeks of initial therapy with prednisone and/or calcineurin
   inhibitor (CNI) ± additional non-sirolimus agent (started at the time of chronic GVHD
   diagnosis).

   - Patient or guardian willing and able to provide informed consent.

   - Stated willingness to use contraception in women of childbearing potential.

   - Stated willingness of patient to comply with study procedures and reporting
   requirements.

Exclusion Criteria:

   - Patients with late persistent acute GVHD or recurrent acute GVHD only.

   - Inability to begin prednisone therapy at a dose of greater than 0.5 mg/kg/day.

   - Receiving sirolimus for treatment of chronic GVHD (sirolimus for prophylaxis or
   treatment of acute GVHD is acceptable).

   - Already receiving sirolimus (for prophylaxis or treatment of acute GVHD) with
   prednisone at ≥ 0.25 mg/kg/day (or equivalent) ± additional agents.

   - Receiving therapy for chronic GVHD for more than 16 weeks.

   - Invasive fungal or viral infection not responding to appropriate antifungal or
   antiviral therapies.

   - Inadequate renal function defined as measured creatinine clearance less than 50
   mL/min/1.73 m^2 based on the Cockcroft-Gault formula (adults) or Schwartz formula (age
   less than or equal to 12 years). Adults: estimated creatinine clearance rate (eCCr)
   (mL/min/) = (140 - age) x mass (kg) x (0.85 if female)/72 x serum creatinine (mg/dL;
   Creatinine clearance (mL/min/1.73m^2) = eCCr x 1.73/Body Surface Area (BSA) (m^2);
   Children: eCCr (mL/min/1.73 m^2) = k x height (cm) / serum creatinine (mg/dL) k = 0.33
   (pre-term), 0.45 (full term to 1 year old), 0.55 (age 1-12 years).

   - Inability to tolerate oral medications.

   - Absolute neutrophil count less than 1500 per microliter.

   - Requirement for platelet transfusions.

   - Pregnancy (positive serum β-HCG) or breastfeeding.

   - Receiving any treatment for persistent, progressive or recurrent malignancy.

   - Progressive or recurrent malignancy defined other than by quantitative molecular
   assays.

   - Known hypersensitivity to sirolimus.