Reprogramming to pluripotency is a low-efficiency process at the population level. Despite notable advances to molecularly characterize key steps, several fundamental aspects remain poorly understood, including when the potential to reprogram is first established. Here, we apply live-cell imaging combined with a novel statistical approach to infer when somatic cells become fated to generate downstream pluripotent progeny. By tracing cell lineages from several divisions before factor induction through to pluripotent colony formation, we find that pre-induction sister cells acquire similar outcomes. Namely, if one daughter cell contributes to a lineage that generates induced pluripotent stem cells (iPSCs), its paired sibling will as well. This result suggests that the potential to reprogram is predetermined within a select subpopulation of cells and heritable, at least over the short term. We also find that expanding cells over several divisions prior to factor induction does not increase the per-lineage likelihood of successful reprogramming, nor is reprogramming fate correlated to neighboring cell identity or cell-specific reprogramming factor levels. By perturbing the epigenetic state of somatic populations with Ezh2 inhibitors prior to factor induction, we successfully modulate the fraction of iPSC-forming lineages. Our results therefore suggest that reprogramming potential may in part reflect preexisting epigenetic heterogeneity that can be tuned to alter the cellular response to factor induction.