We have recently defined a novel population of PD-1 (programmed cell death 1)+ TCF1 (T cell factor 1)+ virus-specific CD8 T cells that function as resource cells during chronic LCMV infection and provide the proliferative burst seen after PD-1 blockade. Such CD8 T cells have been found in other chronic infections and also in cancer in mice and humans. These CD8 T cells exhibit stem-like properties undergoing self-renewal and also differentiating into the terminally exhausted CD8 T cells. Here we compared the epigenetic signature of stem-like CD8 T cells with exhausted CD8 T cells. ATAC-seq analysis showed that stem-like CD8 T cells had a unique signature implicating activity of HMG (TCF) and RHD (NF-κB) transcription factor family members in contrast to higher accessibility to ETS and RUNX motifs in exhausted CD8 T cells. In addition, regulatory regions of the transcription factors Tcf7 and Id3 were more accessible in stem-like cells whereas Prdm1 and Id2 were more accessible in exhausted CD8 T cells. We also compared the epigenetic signatures of the 2 CD8 T cell subsets from chronically infected mice with effector and memory CD8 T cells generated after an acute LCMV infection. Both CD8 T cell subsets generated during chronic infection were strikingly different from CD8 T cell subsets from acute infection. Interestingly, the stem-like CD8 T cell subset from chronic infection, despite sharing key functional properties with memory CD8 T cells, had a very distinct epigenetic program. These results show that the chronic stem-like CD8 T cell program represents a specific adaptation of the T cell response to persistent antigenic stimulation.