This is a single center, single arm, open-label phase 2 study to determine the efficacy of autologous T cells expressing CD19 chimeric antigen receptors expressing tandem TCRζ and 4-1BB (TCRζ/4-1BB) co-stimulatory domains (referred to as "CART19" cells) in adults with minimal residual disease (MRD) during upfront treatment for CD19+ acute lymphoblastic leukemia.