Patients with relapsed leukemia often develop resistance to chemotherapy. For this reason, we are attempting to use a patient's own T cells, which can be genetically modified to expresses a chimeric antigen receptor(CAR). The CAR enables the T cell to recognize and kill the leukemic cells though the recognition of CD19, a protein expressed on the surface of the majority of pediatric ALL. This is a phase I study designed to determine the maximum tolerated dose of the CAR+ T cells and define the toxicity of the treatment. As a secondary aim, we will be looking at the efficacy of the T cells on eradicating the patient's leukemic cells.