After priming, naïve CD8 T lymphocytes establish specific heritable transcription programs that define progression to long-lasting memory cells or to short-lived effector cells. Although lineage specification is critical for protection, it remains unclear how chromatin dynamics contributes to the control of gene expression programs. We explored the role of gene silencing by the histone methyltransferase Suv39h1. In murine CD8 T cells activated after infection, Suv39h1-dependent trimethylation of histone H3 lysine 9 controls the expression of a set of stem cell-related memory genes. Single-cell RNA sequencing revealed a defect in silencing of stem/memory genes selectively in-defective T cell effectors. As a result, -defective CD8 T cells show sustained survival and increased long-term memory reprogramming capacity. Thus, Suv39h1 plays a critical role in marking chromatin to silence stem/memory genes during CD8 T effector terminal differentiation.