Safety and Efficacy Study of Adult Human Mesenchymal Stem Cells to Treat Acute Graft Versus Host Disease (GVHD)

Protocol 260 Inclusion Criteria: * Participant must be 18 to 70 years of age inclusive. * If female and of child-bearing age, participant must be non-pregnant, not breast feeding, and use adequate contraception. Males must use adequate contraception. * Participant must have newly diagnosed, Grade II-IV acute GVHD requiring therapy. Biopsy for confirmation of GVHD is not mandatory, but is recommended when feasible. Enrollment should not be delayed awaiting biopsy results. * Participant must have received either full or reduced intensity myeloablative regimens followed by an allogeneic hematopoietic stem cell transplant using bone marrow, peripheral blood stem cell, or cord blood, including donor lymphocyte infusion (DLI). * Participant must have minimal renal and hepatic function as defined by: \* Calculated creatinine clearance (CLcr) of \> 30 mL/min using the Cockroft-Gault equation. * Participant must be available for all specified assessments at the study site through study Day 28. * Participant must provide written informed consent and authorization for use and disclosure of protected health information (PHI). Protocol 260 Exclusion Criteria: * Participant has received previous treatment for Grade II-IV acute GVHD (except as noted in Criterion 2). * Participant has been treated for GVHD with methylprednisolone, \> 2mg/kg/day, for more than 72 hours prior to receiving Prochymal®. * Participant has uncontrolled alcohol or substance abuse within 6 months of randomization. * Participant has received an investigational agent (not approved by food and drug administration (FDA) for marketed use in any indication) within 30 days of randomization. Participant may not receive an investigational agent during the 28-day study period. * 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 unstable arrhythmia. * Participant is unwilling to sign consent form for the long-term follow-up study, Protocol 261. * Participant has a known allergy to bovine or porcine products. * Participant had received transplant for a solid tumor disease.