BRCA1 deficiencies cause breast, ovarian, prostate and other cancers, and render tumours hypersensitive to poly(ADP-ribose) polymerase (PARP) inhibitors. To understand the resistance mechanisms, we conducted whole-genome CRISPR-Cas9 synthetic-viability/resistance screens in BRCA1-deficient breast cancer cells treated with PARP inhibitors. We identified two previously uncharacterized proteins, C20orf196 and FAM35A, whose inactivation confers strong PARP-inhibitor resistance. Mechanistically, we show that C20orf196 and FAM35A form a complex, 'Shieldin' (SHLD1/2), with FAM35A interacting with single-stranded DNA through its C-terminal oligonucleotide/oligosaccharide-binding fold region. We establish that Shieldin acts as the downstream effector of 53BP1/RIF1/MAD2L2 to promote DNA double-strand break (DSB) end-joining by restricting DSB resection and to counteract homologous recombination by antagonizing BRCA2/RAD51 loading in BRCA1-deficient cells. Notably, Shieldin inactivation further sensitizes BRCA1-deficient cells to cisplatin, suggesting how defining the SHLD1/2 status of BRCA1-deficient tumours might aid patient stratification and yield new treatment opportunities. Highlighting this potential, we document reduced SHLD1/2 expression in human breast cancers displaying intrinsic or acquired PARP-inhibitor resistance.