During infection with an acute microbial infection, responding CD8+ T cells give rise to effector cells that provide acute host defense and memory cells that provide sustained protection. An alternative outcome is exhaustion, a state of T cell dysfunction that occurs in the context of chronic infections and cancer. Although it is evident that exhausted CD8+ T cells (TEX) are phenotypically and molecularly distinct from effector and memory CD8+ T cells, the factors regulating the earliest events in the differentiation process of TEX cells remain incompletely understood. Here we performed single-cell RNA-sequencing and single-cell ATAC-sequencing of CD8+ T cells responding to LCMV-Armstrong (LCMV-Arm) or LCMV-Clone 13 (LCMV-Cl13). Compared to CD8+ T cells that had undergone their first division in response to LCMV-Arm (Div1ARM) cells, CD8+ T cells that had undergone their first division in response to LCMV-Cl13 (Div1CL13) expressed higher levels of genes encoding transcription factors that have been previously reported to promote exhaustion, along with Ezh2, the catalytic component of the polycomb repressive complex 2 (PRC2) complex which mediates epigenetic silencing. Modulation of Ezh2 by genetic deletion or retroviral overexpression approaches resulted in decreased or increased expression, respectively, of exhaustion-associated molecules by CD8+ T cells responding to LCMV-Cl13. Taken together, these findings indicate that acquisition of phenotypic, transcriptional, and epigenetic features associated with T cell exhaustion can occur earlier than previously appreciated and raise the possibility that TEX cells may not need to transit through an effector intermediate state.