Thymoglobulin to Prevent Acute Graft vs. Host Disease (GvHD) in Patients With Acute Lymphocytic Leukemia (ALL) or Acute Myelogenous Leukemia (AML) Receiving a Stem Cell Transplant

Inclusion Criteria: * Subject has an HLA-A, -B and -DRB1 identical related donor and must be fully matched at Class II. A high resolution molecular HLA typing (at least 4 digits) is mandatory for HLA Class II and optional for HLA Class I * Subject has confirmed diagnosis of acute myeloid leukemia (AML) or acute lymphoblastic leukemia (ALL) with acute myeloid leukemia (including secondary leukemia) in first complete remission (CR2) or acute lymphoid in CR1 or CR2. * Subject is \>= 18 and \<= 55 years of age. * Subject is receiving a myeloablative-conditioning regimen * Men and women of childbearing age potential agree to practice an acceptable and reliable form of contraception during the study. Women must not be lactating or pregnant, and must have a negative serum pregnancy test. * Subject has been fully informed and has signed an IRB-approved informed consent form. * Subject is willing and able to follow study procedures for the 6 months post-transplant. * The subject must be serologically negative for human immunodeficiency virus (HIV). * Subject agrees to be followed for possible long-term safety outcomes for up to 12 months post-transplant. * Subject has an ECOG performance score of 0-2. * Subject has a creatinine of \< 2.0mg/dL or creatinine clearance of \> 50mL/min. * Subject has an ejection fraction of \>= 40% * Subject has a serum bilirubin of \< 2mg/dL. Exclusion Criteria: * Subject is receiving fludarabine, a non-myeloablative regimen, or other purine analogues as part of the conditioning regimen. * Subject is receiving an ex vivo engineered or processed graft (CD34+ enrichment, T-cell depletion, etc.) * Subject has documented uncontrolled central nervous system (CNS) disease. * Subject is expected to receive or has received methotrexate for GvHD prophylaxis. * Subject has alanine aminotransferase (ALT)or aspartate aminotransferase (AST) level of \> 3x the upper limit of normal range within 3 weeks prior to transplant. * Subject has used any experimental agent within 30 days prior to the date of signing the informed consent. * Subject is receiving or has received a bone marrow transplant from a donor who has positive serology for HIV, hepatitis B virus(HBV), hepatitis C virus (HCV) or syphilis. * Subject has a known contraindication to administration of rabbit anti-thymocyte globulin. * Subject is currently abusing drugs or alcohol or, in the opinion of the Investigator, is at high risk for poor compliance. * Subject, who in the opinion of the Investigator, has significant medical or psychological problems that warrants exclusion. Examples of significant problems include, but are not limited to, morbid obesity or severe cardiac disease.