The timing of cell production by progenitor cells is an essential aspect of development. Particularly during neurogenesis, the time at which neurons and glia are produced affects their function and proper integration into neural circuits. In both the mammalian and Drosophila central nervous system, neural progenitors progressively lose competence to make early-born cell types, so that “old” progenitors can no longer be induced to make “young” neurons. My dissertation work used Drosophila neural progenitors, known as neuroblasts, as a model to investigate the restriction of neural progenitor competence. Drosophila neuroblasts sequentially express temporal transcription factors (TTFs) that determine neural and glial cell fate based on birth-order. For example, the second TTF in the series, Kruppel, is necessary and sufficient for all second-born / third-born fates, regardless of cell type or neuroblast lineage. However, neuroblasts lose competence to respond to Kruppel with each division, ultimately completely losing competence to produce Kruppel-specified cell types at late stages of development. I discovered that chromatin remodeling complexes of the Polycomb group are necessary and sufficient for the temporal restriction of neuroblast competence. I found that Polycomb complexes establish distinct competence windows in neuroblasts that transition from early motorneuron production to late interneuron production. This work provides a mechanistic basis for the restriction of neuroblast competence and supports a model in which Polycomb complexes progressively limit the ability of TTFs to activate gene expression programs that induce early-born fates.