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This is a randomized, open-label, parallel group study to determine the optimal dose of CART-19 cells (of the two dose levels being assessed (1-5x10xE8 vs. 1-5x10xE7 CART-19 cells). This trial will be conducted in two stages. In Stage 2, the selected dose cohort will be expanded to enroll additional subjects, to ensure that a total of 20 evaluable subjects are treated at that dose level. Based on the Stage 1 analysis performed in November 2014, Arm 1 was chosen for expansion in Stage 2. Stage 2 dose will be 1-5x10xE8 transduced CART-19 cells. The dose of 1-5 x 10xE8 T-cells in Stage 2 will be administered via split dosing: 10% on Day 1 (1-5x10xE7), 30% on Day 2 (3x107-1.5x10xE8), 60% on Day 3 (6x107-3x10xE8). Evaluable subjects are defined as those who were able to receive the viable product at the intended dose level and have completed at least 3 months of follow-up after the first infusion, or have discontinued early due to disease progression, initiation of a new cancer therapy, or death. This protocol also allows for the retreatment of any subject who had an initial response to their 1st infusion, lost detectable CART19 cells, and has subsequently relapsed. The target dose for this retreatment cohort is 1-5 x 10xE8 CART19 cells. The minimum acceptable dose for infusion is 1 x 10xE7 CART19 cells. Subjects originally treated under Stage 1 will receive a single infusion, if sufficient CART19 product remains. For patients from Stage 1 who do not have a sufficient dose remaining, subjects will be remanufactured under Stage 2 conditions and receive the split dose. Subjects originally treated under Stage 2 will also receive the split dose for retreatment.