Nonrandom DNA segregation (NDS) is a mitotic event in which sister chromatids carrying the oldest DNA strands are inherited exclusively by one of the two daughter cells. Although this phenomenon has been observed across various organisms, the mechanism and physiological relevance of this event remain poorly defined. Here, we demonstrate that DNA replication stress can trigger NDS in human cells. This biased inheritance of old template DNA is associated with the asymmetric DNA damage response (DDR), which derives at least in part from telomeric DNA. Mechanistically, we reveal that the ATR/CHK1 signaling pathway plays an essential role in mediating NDS. We show that this biased segregation process leads to cell-cycle arrest and cell death in damaged daughter cells inheriting newly replicated DNA. These data therefore identify a key role for NDS in the maintenance of genomic integrity within cancer cell populations undergoing replication stress due to oncogene activation.