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

Inclusion Criteria: * Participant must be 6 months to 70 years of age, inclusive. * Participants who have failed to respond to steroid treatment. Failure to respond to steroid treatment is defined as any grade B-D (IBMTR) grading of acute GVHD that shows: * No improvement after 3 days and a duration of no greater than 2 weeks while receiving treatment with methylprednisolone (greater than or equal to 1 mg/kg/day) or equivalent. * Participant must be treated within 4 days of randomization. In urgent situations 2nd line therapy may be started 24 hours prior to randomization, and Prochymal® must be initiated within the following 3 days. * Participants who have received an increase in their steroid dose treatment prior to randomization will be eligible for enrollment. An increase in steroid dose will not be considered as second line therapy. * Participant must have adequate renal function as defined by: Calculated Creatinine Clearance of \>30 milliliters per minute (mL/min) using the Cockcroft-Gault equation. * For pediatric participants: Schwartz equation: (Participant population: infants over 1 week old through adolescence (\<18 years old). * Participants who are women of childbearing potential must be non-pregnant, not breast-feeding, and use adequate contraception. Male participants must use adequate contraception. * Participant must have a minimum Karnofsky Performance Level of at least 30 at the time of study entry. * Participant (or legal representative where appropriate) must be capable of providing written informed consent. Exclusion Criteria: * Participant has started treatment with second line therapy \>24 hours prior to randomization. * Participant has received agents other than steroids for primary treatment of acute GVHD. * Participant is participating in the CTN Protocol 0302. * 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 including uncontrolled infection, heart failure, pulmonary hypertension, etc. * Participant may not receive any other investigational agents (not approved by the FDA) concurrently during study participation or within 30 days of randomization. * Participant has a known allergy to bovine or porcine products. * Participant has received a transplant for a solid tumor disease.