Study of KTE-X19 in Minimal Residual Disease (MRD) Positive B-Cell Acute Lymphoblastic Leukemia (B-ALL)

Inclusion Criteria: * Must be an adult 18 years of age or older. * Pathologically confirmed CD19 positive B-cell acute lymphoblastic leukemia. * Treatment and full recovery from induction chemotherapy, with following exceptions: A. Vincristine associated grade 1 peripheral neuropathy B. Steroid/asparaginase associated diabetes and/or hypertension C. Inotuzumab/chemotherapy associated cytopenias * Patients must be in a complete remission with Minimal Residual Disease (MRD) following an induction regimen. MRD is defined herein as a bone marrow biopsy with fewer than 5% lymphoblasts. Complete remission implies the resolution of any extramedullary and/or Central Nervous Syndrome (CNS)-2-3/parenchymal disease. * Be willing and able to provide written informed consent/assent for the trial. * Able to adhere to the study visit schedule and other protocol requirements. * Eastern Cooperative Oncology Group (ECOG) performance status 0-1. * Adequate renal, hepatic, pulmonary, cardiac function. * Adequate hematopoietic reserve. * Females of childbearing potential (FCBP) must have a negative serum pregnancy test at screening. A FCBP is considered when a sexually mature female: 1\) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 12 consecutive months. * Subjects of both genders of child-bearing potential must be willing to practice birth control from the time of consent through 6 months after the completion of KTE-X19 infusion. Exclusion Criteria: * Diagnosis of L3 type Burkitt's lymphoma, Mixed-Lineage Leukemia (MLL) rearranged leukemia, biphenotypic leukemia, mixed phenotype acute leukemia, blast phase of chronic myeloid leukemia, or stem-cell leukemia. * Any active infection requiring systemic therapy, including HIV, Hepatitis B, and/or Hepatitis C. * History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator (including but not limited to unstable angina, pre-existing liver disease, recurrent pancreatitis, uncontrolled diabetes, hypertriglyceridemia, pulmonary hypertension, or severe Congestive Heart Failure (CHF). * Recurrent thrombosis, or non-central venous catheter associated thrombosis within 3 months prior to enrollment. * History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, or other clinically significant cardiac disease within 12 months of enrollment. * History or presence of any CNS disorder such as a seizure disorder, cerebrovascular ischemia/hemorrhage, dementia, cerebellar disease, any autoimmune disease with CNS involvement, posterior reversible encephalopathy syndrome (PRES), or cerebral edema. * Active CNS/leptomeningeal leukemia. * Severe comorbid conditions for which life expectancy would be \<6 months. * Patients with active (uncontrolled, metastatic) second malignancies are excluded. * History of concomitant genetic syndrome associated with bone marrow failure such as Fanconi anemia, Kostmann syndrome, Shwachman-Diamond syndrome. * Primary immunodeficiency or history of autoimmune disease (Crohns, rheumatoid arthritis, systemic lupus) resulting in end organ injury or requiring systemic immunosuppression/systemic disease modifying agents within the last 2 years. * Corticosteroid therapy at a pharmacologic dose (\> 5 mg/day of prednisone or equivalent doses of other corticosteroids) and other immunosuppressive drugs must be avoided for 7 days prior to enrollment. * Presence of any indwelling line or drain (percutaneous nephrostomy tube, indwelling Foley catheter, biliary drain, or pleural/peritoneal/pericardial catheter). Ommaya reservoirs and dedicated central venous access catheters such as a Port-a-Cath or Hickman catheter are permitted. * Live vaccine ≤ 4 weeks prior to enrollment. * Pregnant, breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 3 months after the last dose of trial treatment.