Stem/progenitor cells often generate distinct cell types in a stereotyped birth order, and over time lose competence to specify earlier-born fates by unknown mechanisms. In Drosophila, the Hunchback transcription factor acts in neural progenitors (neuroblasts) to specify early-born neurons, in part by indirectly inducing the neuronal transcription of its target genes, including the hunchback gene. We used in vivo immuno-DNA FISH and found that the hunchback gene moves to the neuroblasts nuclear periphery, a repressive subnuclear compartment, precisely when competence to specify early-born fate is lost, and several hours and cell divisions following termination of its transcription. Hunchback movement to the lamina correlated with down regulation of the neuroblasts nuclear protein, distal antenna (Dan). Either prolonging Dan expression or disrupting lamina interfered with hunchback repositioning and extended neuroblasts competence. We propose that neuroblasts undergo a developmentally-regulated subnuclear genome reorganization to permanently silence Hunchback target genes that results in loss of progenitor competence.