Postembryonic neuroblasts are stem cell-like precursors that generate most neurons of the adult Drosophila central nervous system (CNS). Their capacity to divide is modulated along the anterior-posterior body axis, but the mechanism underlying this is unclear. We use clonal analysis of identified precursors in the abdomen to show that neuron production stops because the cell death program is activated in the neuroblast while it is still engaged in the cell cycle. A burst of expression of the Hox protein Abdominal-A (AbdA) specifies the time at which apoptosis occurs, thereby determining the final number of progeny that each neuroblast generates. These studies identify a mechanism linking the Hox axial patterning system to neural proliferation, and this involves temporal regulation of precursor cell death rather than the cell cycle.