Chordoma is a malignant, often incurable bone tumour showing notochordal differentiation. Here, we defined the somatic driver landscape of 104 cases of sporadic chordoma. We reveal somatic duplications of the notochordal transcription factor brachyury (T) in up to 27% of cases. These variants recapitulate the rearrangement architecture of the pathogenic germline duplications of T that underlie familial chordoma. In addition, we find potentially clinically actionable PI3K signalling mutations in 16% of cases. Intriguingly, one of the most frequently altered genes, mutated exclusively by inactivating mutation, was LYST (10%), which may represent a novel cancer gene in chordoma.