PD-1+TCF-1+ stem-like CD8 T cells act as critical resource cells for maintaining T cell immunity in chronic viral infections and cancer. In addition, they provide the proliferative burst of effector CD8 T cells after programmed death protein 1 (PD-1)-directed immunotherapy. However, it is not known whether checkpoint blockade diminishes the number of these stem-like progenitor cells as effector cell differentiation increases. To investigate this, we used the mouse model of chronic lymphocytic choriomeningitis virus (LCMV) infection. Treatment of chronically infected mice with either αPD-1 or αPD-L1 antibody not only increased effector cell differentiation from the virus-specific stem-like CD8 T cells but also increased their proliferation so their numbers were maintained. The increased self-renewal of LCMV-specific stem-like CD8 T cells was mTOR dependent. We used microscopy to understand the division of these progenitor cells and found that after PD-1 blockade, an individual dividing cell could give rise to a differentiated TCF-1- daughter cell alongside a self-renewing TCF-1+ sister cell. This asymmetric division helped to preserve the number of stem-like cells. Moreover, we found that the PD-1+TCF-1+ stem-like CD8 T cells retained their transcriptional program and their in vivo functionality in terms of responding to viral infection and to repeat PD-1 blockade. Together, our results demonstrate that PD-1 blockade does not deplete the stem-like population despite increasing effector differentiation. These findings have implications for PD-1-directed immunotherapy in humans.