Clinical success with poly (ADP-ribose) polymerase inhibitors (PARPi) is impeded by inevitable resistance and associated cytotoxicity. Depletion of Amplified in Liver Cancer 1 (ALC1), a chromatin-remodeling enzyme, can overcome these limitations by hypersensitizing BReast CAncer genes 1/2 (BRCA1/2) mutant cells to PARPi. Here, we demonstrate that PARPi hypersensitivity upon ALC1 loss is reliant on its role in promoting the repair of chromatin buried abasic sites. We show that ALC1 enhances the ability of the abasic site processing enzyme, Apurinic/Apyrimidinic endonuclease 1 (APE1) to cleave nucleosome-occluded abasic sites. However, unrepaired abasic sites in ALC1-deficient cells are readily accessed by APE1 at the nucleosome-free replication forks. APE1 cleavage leads to fork breakage and trapping of PARP1/2 upon PARPi treatment, resulting in hypersensitivity. Collectively, our studies reveal how cells overcome the chromatin barrier to repair abasic lesions and uncover cleavage of abasic sites as a mechanism to overcome limitations of PARPi.