Maintenance chemotherapy with 6-mercaptopurine and methotrexate, widely believed an essential contribution to the high cure rates achieved in children with acute lymphoblastic leukaemia (ALL), is thought to work by killing the leukaemia cells that remain after intensive chemotherapy. We suggest instead that ALL commonly arises in precursor B cells normally programmed to die, and that maintenance chemotherapy does not kill these cells but controls growth of the leukaemia clone so that programmed death can occur. A similar approach may apply to other cancers in which programmed death is intrinsic to the normal counterparts of the neoplastic cells.