In cancer and infections, self-renewing stem-like CD8+ T cells mediate the response of immunotherapies and replenish terminally exhausted T cells and effector-like T cells. However, the programs governing the lineage choice in chimeric antigen receptor (CAR) T cells are unclear. Here, by simultaneously profiling single-cell chromatin accessibility and transcriptome in the same CAR T cells, we identified heterogeneous chromatin states within CD8+ T cell subsets that foreshadowed transcriptional changes and were primed for regulation by distinct transcription factors. Transcription factors that controlled each CD8+ T cell subset were regulated by high numbers of enhancers and positioned as hubs of gene networks. FOXP1, a hub in the stem-like network, promoted expansion and stemness of CAR T cells and limited excessive effector differentiation. In the effector network, KLF2 enhanced effector CD8+ T cell differentiation and prevented terminal exhaustion. Thus, we identified gene networks and hub transcription factors that controlled the differentiation of stem-like CD8+ CAR T cells into effector or exhausted CD8+ CAR T cells.