Progenitors are early lineage cells that proliferate before the onset of terminal differentiation. Although widespread, the epigenetic mechanisms that control the progenitor state and the onset of differentiation remain elusive. By studying Drosophila ovarian follicle cell progenitors, we identified lysine-specific demethylase 1 (lsd1) and CoRest as differentiation regulators using a GAL4∷GFP variegation assay. The follicle cell progenitors in lsd1 or CoRest heterozygotes prematurely lose epigenetic plasticity, undergo the Notch-dependent mitotic-endocycle transition, and stop dividing before a normal number of follicle cells can be produced. Simultaneously reducing the dosage of the histone H3K4 methyltransferase Trithorax reverses these effects, suggesting that an Lsd1/CoRest complex times progenitor differentiation by controlling the stability of H3K4 methylation levels. Individual cells or small clones initially respond to Notch; hence, a critical level of epigenetic stabilization is acquired cell-autonomously and initiates differentiation by making progenitors responsive to pre-existing external signals.