Induction of cell-autonomous apoptosis following oncogene-induced overproliferation is a major tumor-suppressive mechanism in vertebrates. However, the detailed mechanism mediating this process remains enigmatic. In this study, we demonstrate that dMyc-induced cell-autonomous apoptosis in the fruit fly Drosophila melanogaster relies on an intergenic sequence termed the IRER (irradiation-responsive enhancer region). The IRER mediates the expression of surrounding proapoptotic genes, and we use an in vivo reporter of the IRER chromatin state to gather evidence that epigenetic control of DNA accessibility within the IRER is an important determinant of the strength of this response to excess dMyc. In a previous work, we showed that the IRER also mediates P53-dependent induction of proapoptotic genes following DNA damage, and the chromatin conformation within IRER is regulated by polycomb group-mediated histone modifications. dMyc-induced apoptosis and the P53-mediated DNA damage response thus overlap in a requirement for the IRER. The epigenetic mechanisms controlling IRER accessibility appear to set thresholds for the P53- and dMyc-induced expression of apoptotic genes in vivo and may have a profound impact on cellular sensitivity to oncogene-induced stress.