The BRCA1–BARD1 tumour suppressor is an E3 ubiquitin ligase necessary for the repair of DNA double-strand breaks by homologous recombination^{, , , , , , , , –}. The BRCA1–BARD1 complex localizes to damaged chromatin after DNA replication and catalyses the ubiquitylation of histone H2A and other cellular targets^{, , –}. The molecular bases for the recruitment to double-strand breaks and target recognition of BRCA1–BARD1 remain unknown. Here we use cryo-electron microscopy to show that the ankyrin repeat and tandem BRCT domains in BARD1 adopt a compact fold and bind to nucleosomal histones, DNA and monoubiquitin attached to H2A amino-terminal K13 or K15, two signals known to be specific for double-strand breaks^,. We further show that RING domains in BRCA1–BARD1 orient an E2 ubiquitin-conjugating enzyme atop the nucleosome in a dynamic conformation, primed for ubiquitin transfer to the flexible carboxy-terminal tails of H2A and variant H2AX. Our work reveals a regulatory crosstalk in which recognition of monoubiquitin by BRCA1–BARD1 at the N terminus of H2A blocks the formation of polyubiquitin chains and cooperatively promotes ubiquitylation at the C terminus of H2A. These findings elucidate the mechanisms of BRCA1–BARD1 chromatin recruitment and ubiquitylation specificity, highlight key functions of BARD1 in both processes and explain how BRCA1–BARD1 promotes homologous recombination by opposing the DNA repair protein 53BP1 in post-replicative chromatin^{, , , –}. These data provide a structural framework to evaluate BARD1 variants and help to identify mutations that drive the development of cancer.