The precise pathways of memory T-cell differentiation are incompletely understood. Here we exploit transgenic mice expressing fluorescent cell cycle indicators to longitudinally track the division dynamics of individual CD8⁺ T cells. During influenza virus infection in vivo, naive T cells enter a CD62L^intermediate state of fast proliferation, which continues for at least nine generations. At the peak of the anti-viral immune response, a subpopulation of these cells markedly reduces their cycling speed and acquires a CD62L^hi central memory cell phenotype. Construction of T-cell family division trees in vitro reveals two patterns of proliferation dynamics. While cells initially divide rapidly with moderate stochastic variations of cycling times after each generation, a slow-cycling subpopulation displaying a CD62L^hi memory phenotype appears after eight divisions. Phenotype and cell cycle duration are inherited by the progeny of slow cyclers. We propose that memory precursors cell-intrinsically modulate their proliferative activity to diversify differentiation pathways.