Gain-of-function (GOF) p53 mutations are observed frequently in most intractable human cancers and establish dependency for tumor maintenance and progression. While some of the genes induced by GOF p53 have been implicated in more rapid cell proliferation compared with p53-null cancer cells, the mechanism for dependency of tumor growth on mutant p53 is unknown. This report reveals a therapeutically targetable mechanism for GOF p53 dependency. We have shown that GOF p53 increases DNA replication origin firing, stabilizes replication forks, and promotes micronuclei formation, thus facilitating the proliferation of cells with genomic abnormalities. In contrast, absence or depletion of GOF p53 leads to decreased origin firing and a higher frequency of fork collapse in isogenic cells, explaining their poorer proliferation rate. Following genome-wide analyses utilizing ChIP-Seq and RNA-Seq, GOF p53–induced origin firing, micronuclei formation, and fork protection were traced to the ability of GOF p53 to transactivate cyclin A and CHK1. Highlighting the therapeutic potential of CHK1’s role in GOF p53 dependency, experiments in cell culture and mouse xenografts demonstrated that inhibition of CHK1 selectively blocked proliferation of cells and tumors expressing GOF p53. Our data suggest the possibility that checkpoint inhibitors could efficiently and selectively target cancers expressing GOF p53 alleles.