Reversing the dysfunctional T cell state that arises in cancer and chronic viral infections is the focus of therapeutic interventions; however, current therapies are effective in only some patients and some tumor types. To gain a deeper molecular understanding of the dysfunctional T cell state, we analyzed population and single-cell RNA profiles of CD8(+) tumor-infiltrating lymphocytes (TILs) and used genetic perturbations to identify a distinct gene module for T cell dysfunction that can be uncoupled from T cell activation. This distinct dysfunction module is downstream of intracellular metallothioneins that regulate zinc metabolism and can be identified at single-cell resolution. We further identify Gata-3, a zinc-finger transcription factor in the dysfunctional module, as a regulator of dysfunction, and we use CRISPR-Cas9 genome editing to show that it drives a dysfunctional phenotype in CD8(+) TILs. Our results open novel avenues for targeting dysfunctional T cell states while leaving activation programs intact.