This study is designed to evaluate the safety and efficacy of Prochymal® (Ex-vivo Cultured Adult Human Mesenchymal Stem Cells) in participants experiencing treatment-refractory acute GVHD, Grades III-IV, that is refractory to standard first-line therapies and at least one second-line therapy.

Allogeneic HSCT is used in the treatment of a variety of hematological, myeloproliferative and lymphoproliferative disorders, and malignancies involving solid tumors. Participants receiving HSCT can develop a life-threatening condition called GVHD. GVHD occurs when donor T cells from the donor bone marrow recognize host cells as "foreign" and initiate an inflammatory immunological response. The standard of care for treatment of acute GVHD consists of intravenous delivery of methylprednisolone starting on Day 1 and continuation of either cyclosporine or tacrolimus. This regimen of steroids and immunosuppressive drugs may relieve symptoms of GVHD, but some participants are refractory to current standard of care treatment. For treatment-refractory participants with grades III-IV GVHD mortality is approximately 80%. A therapy that could effectively suppress the immunological response from GVHD and help repair the damaged tissue could significantly decrease the mortality rate from this disease.

Inclusion Criteria:

• Participants must be 6 months to 70 years of age inclusive.
• If female and of childbearing age, participants must be non-pregnant, not breast-feeding, and use adequate contraception. Male participants must use adequate contraception.
• Participants must have Grade III-IV acute GVHD that has failed to respond to standard first and at least one second-line therapy. Biopsy for confirmation of both skin and gastrointestinal GVHD is not mandatory, but is recommended when feasible. Enrollment should not be delayed awaiting biopsy results.
• Participants must have minimal renal function as defined by: Calculated creatinine clearance (CrCl) of > 30 milliliters/minute (mL/min) using the Cockcroft-Gault equation.
• Participant must provide written informed consent and authorization for use and disclosure of protected health information (PHI).

Exclusion Criteria:

• Participant has uncontrolled alcohol or substance abuse within 6 months of treatment.
• Participant has any underlying or current medical or psychiatric condition that, in the opinion of the Investigator, would interfere with the evaluation of the participant (e.g., uncontrolled infection, right heart failure, pulmonary hypertension, etc.).
• Participant has a clinically significant, unstable arrhythmia.
• Participant has a known allergy to bovine or porcine products.
• Participant is unwilling to sign consent form for the long-term follow-up study, protocol 271.