Chemotherapy is used to treat most cancer patients, yet our understanding of factors that dictate response and resistance to such drugs remains limited. We report the generation of a quantitative chemical-genetic interaction map in human mammary epithelial cells charting the impact of the knockdown of 625 genes related to cancer and DNA repair on sensitivity to 29 drugs, covering all classes of chemotherapy. This quantitative map is predictive of interactions maintained in other cell lines, identifies DNA-repair factors, predicts cancer cell line responses to therapy, and prioritizes synergistic drug combinations. We identify that ARID1A loss confers resistance to PARP inhibitors in cells and ovarian cancer patients and that loss of GPBP1 causes resistance to cisplatin and PARP inhibitors through the regulation of genes involved in homologous recombination. This map helps navigate patient genomic data and optimize chemotherapeutic regimens by delineating factors involved in the response to specific types of DNA damage.