Dysfunction in T cells limits the efficacy of cancer immunotherapy. We profiled the epigenome, transcriptome, and enhancer connectome of exhaustion-prone GD2-targeting HA-28z chimeric antigen receptor (CAR) T cells and control CD19-targeting CAR T cells, which present less exhaustion-inducing tonic signaling, at multiple points during their ex vivo expansion. We found widespread, dynamic changes in chromatin accessibility and three-dimensional (3D) chromosome conformation preceding changes in gene expression, notably at loci proximal to exhaustion-associated genes such as PDCD1, CTLA4, and HAVCR2, and increased DNA motif access for AP-1 family transcription factors, which are known to promote exhaustion. Although T cell exhaustion has been studied in detail in mice, we find that the regulatory networks of T cell exhaustion differ between species and involve distinct loci of accessible chromatin and cis-regulated target genes in human CAR T cell exhaustion. Deletion of exhaustion-specific candidate enhancers of PDCD1 suppress the expression of PD-1 in an in vitro model of T cell dysfunction and in HA-28z CAR T cells, suggesting enhancer editing as a path forward in improving cancer immunotherapy.