Histone deacetylases (HDACs) comprise a family of 18 epigenetic modifiers. The biologically relevant functions of HDAC10 in leukemia cells are enigmatic. We demonstrate that human cultured and primary acute B-cell/T-cell leukemia and lymphoma cells require HDAC10 for their survival. In such cells, HDAC10 controls a MYC-dependent transcriptional induction of the DNA polymerase subunit POLD1. Consequently, pharmacological inhibition of HDAC10 causes DNA breaks and an accumulation of poly-ADP-ribose chains. These processes culminate in caspase-dependent apoptosis. These data reveal a nuclear function for HDAC10. HDAC10 controls the MYC-POLD1 axis to maintain the processivity of DNA replication and genome integrity. This mechanistically defined “HDAC10ness” could prospectively be exploited as treatment option for hematopoietic malignancies.