Pluripotency can be induced in somatic cells by the expression of the four "Yamanaka" factors OCT4, KLF4, SOX2, and MYC. However, even in homogeneous conditions, usually only a rare subset of cells admit reprogramming, and the molecular characteristics of this subset remain unknown. Here, we apply retrospective clone tracing to identify and characterize the individual human fibroblast cells that are primed for reprogramming. These fibroblasts showed markers of increased cell cycle speed and decreased fibroblast activation. Knockdown of a fibroblast activation factor identified by our analysis led to increased reprogramming efficiency, identifying it as a barrier to reprogramming. Changing the frequency of reprogramming by inhibiting the activity of LSD1 led to an enlarging of the pool of cells that were primed for reprogramming. Our results show that even homogeneous cell populations can exhibit heritable molecular variability that can dictate whether individual rare cells will reprogram or not.