Breast Cancer Type 1 Susceptibility Protein (BRCA1)-deficient cells have compromised DNA repair and are sensitive to poly(ADP-ribose) polymerase (PARP) inhibitors. Despite initial responses, the development of resistance limits clinical efficacy. Mutations in the BRCA C-terminal (BRCT) domain of BRCA1 frequently create protein products unable to fold that are subject to protease-mediated degradation. Here, we show HSP90-mediated stabilization of a BRCT domain mutant BRCA1 protein under PARP inhibitor selection pressure. The stabilized mutant BRCA1 protein interacted with PALB2-BRCA2-RAD51, was essential for RAD51 focus formation, and conferred PARP inhibitor as well as cisplatin resistance. Treatment of resistant cells with the HSP90 inhibitor 17-dimethylaminoethylamino-17-demethoxygeldanamycin reduced mutant BRCA1 protein levels and restored their sensitivity to PARP inhibition. Resistant cells also acquired a TP53BP1 mutation that facilitated DNA end resection in the absence of a BRCA1 protein capable of binding CtIP. Finally, concomitant increased mutant BRCA1 and decreased 53BP1 protein expression occur in clinical samples of BRCA1-mutated recurrent ovarian carcinomas that have developed resistance to platinum. These results provide evidence for a two-event mechanism by which BRCA1-mutant tumors acquire anticancer therapy resistance.