Patients with relapsed or refractory leukemia often develop resistance to chemotherapy. For this reason, we are attempting to use T cells obtained directly from the patient, which can be genetically modified to express a chimeric antigen receptor (CAR). The CAR enables the T cell to recognize and kill the leukemic cell through the recognition of CD19, a protein expressed of the surface of the leukemic cell in patients with CD19+ leukemia. This is a phase 1/2 study designed to determine the maximum tolerated dose of the CAR+ T cells as well as to determine the efficacy. The phase 1 cohort is restricted to those patients who have already had an allogeneic hematopoietic cell transplant (HCT). The phase 2 is open to all patients regardless of having a history of HCT.