Suppression of single-stranded DNA (ssDNA) gap accumulation at replication forks has emerged as a potential determinant of chemosensitivity in homologous recombination (HR)-deficient tumors, as ssDNA gaps are transformed into cytotoxic double-stranded DNA breaks. We have previously shown that the histone chaperone CAF-1’s nucleosome deposition function is vital to preventing degradation of stalled replication forks correlating with HR-deficient cells’ response to genotoxic drugs. Here we report that the CAF-1–ASF1 pathway promotes ssDNA gap accumulation at replication forks in both wild-type and breast cancer (BRCA)-deficient backgrounds. We show that this is independent of CAF-1’s nucleosome deposition function but instead may rely on its proper localization to replication forks. Moreover, we show that the efficient localization to nascent DNA of PrimPol, the enzyme responsible for repriming upon replication stress, is dependent on CAF-1. As PrimPol has been shown to be responsible for generating ssDNA gaps as a byproduct of its repriming function, CAF-1’s role in its recruitment could directly impact ssDNA gap formation. We also show that chemoresistance observed in HR-deficient cells when CAF-1 or ASF1A are lost correlates with suppression of ssDNA gaps rather than protection of stalled replication forks. Overall, this work identifies an unexpected role of CAF-1 in regulating PrimPol recruitment and ssDNA gap generation.