The poly(ADP-ribose) polymerase inhibitor (PARPi) class of drugs represents a remarkable advance in the treatment of patients with homologous recombination-deficient tumours, but resistance remains a challenge. Although most research has focused on the downstream consequences of PARPi exposure to tackle resistance, the immediate effect of PARP inhibition on the chromatin environment and its contribution to PARPi toxicity remains elusive. Here we show that PARP inhibition induces histone release from the chromatin. This presents a vulnerability of PARPi-resistant cancer cells, which require histone homeostasis mechanisms to sustain elevated DNA replication rates and survival. Through functional genetic screens, we identified NASP as a key factor in maintaining the stability of evicted histones via its TPR motifs. Loss of NASP renders tumour cells hypersensitive to PARPi treatment in vitro and in vivo, impairs replication fork progression and elevates levels of replication-associated DNA damage. Moreover, NASP acts together with the INO80 complex and the chaperoning activity of PARP1 to ensure efficient histone turnover and prevent the accumulation of lethal DNA damage. Collectively, our work reports on histone eviction as an immediate cellular response to PARPi treatment and provides a promising avenue for targeting histone supply pathways to overcome PARPi resistance.