Precise control of cell death in the nervous system is essential for development. Spatial and temporal factors activate the death of Drosophila neural stem cells (neuroblasts) by controlling the transcription of multiple cell death genes through a shared enhancer. The activity of this enhancer is controlled by abdominal A and Notch, but additional inputs are needed for proper specificity. Here, we show that the Cut DNA binding protein is required for neuroblast death, regulating reaper and grim downstream of the shared enhancer and of abdominal A expression. The loss of cut accelerates the temporal progression of neuroblasts from a state of low overall levels of H3K27me3 to a higher H3K27me3 state. This is reflected in an increase in H3K27me3 modifications in the cell death gene locus in the CNS on Cut knockdown. We also show that cut regulates the expression of the cohesin subunit Stromalin. Stromalin and the cohesin regulatory subunit Nipped-B are required for neuroblast death, and knockdown of Stromalin increases H3K27me3 levels in neuroblasts. Thus, Cut and cohesin regulate apoptosis in the developing nervous system by altering the chromatin landscape.