Chordomas are rare bone tumors with few therapeutic options. Here we show, using whole-exome and genome sequencing within a precision oncology program, that advanced chordomas (n = 11) may be characterized by genomic patterns indicative of defective homologous recombination (HR) DNA repair and alterations affecting HR-related genes, including, for example, deletions and pathogenic germline variants of BRCA2, NBN, and CHEK2. A mutational signature associated with HR deficiency was significantly enriched in 72.7% of samples and co-occurred with genomic instability. The poly(ADP-ribose) polymerase (PARP) inhibitor olaparib, which is preferentially toxic to HR-incompetent cells, led to prolonged clinical benefit in a patient with refractory chordoma, and whole-genome analysis at progression revealed a PARP1 p.T910A mutation predicted to disrupt the autoinhibitory PARP1 helical domain. These findings uncover a therapeutic opportunity in chordoma that warrants further exploration, and provide insight into the mechanisms underlying PARP inhibitor resistance.