T cells engineered to express chimeric antigen receptors (CARs) targeting CD19 have demonstrated impressive activity against relapsed or refractory B-cell cancers yet fail to induce durable remissions for nearly half of all patients treated. Enhancing the efficacy of this therapy requires detailed understanding of the molecular circuitry that restrains CAR-driven antitumor T-cell function. We developed and validated an in vitro model that drives T-cell dysfunction through chronic CAR activation and interrogated how CAR costimulatory domains, central components of CAR structure and function, contribute to T-cell failure. We found that chronic activation of CD28-based CARs results in activation of classical T-cell exhaustion programs and development of dysfunctional cells that bear the hallmarks of exhaustion. In contrast, 41BB-based CARs activate a divergent molecular program and direct differentiation of T cells into a novel cell state. Interrogation using CAR T cells from a patient with progressive lymphoma confirmed the activation of this novel program in a failing clinical product. Furthermore, we demonstrate that 41BB-dependent activation of the transcription factor FOXO3 is directly responsible for impairing CAR T-cell function. These findings identify that costimulatory domains are critical regulators of CAR-driven T-cell failure and that targeted interventions are required to overcome costimulation-dependent dysfunctional programs.