Cell competition is an emerging principle underlying selection for cellular fitness during development and disease. Competition may be relevant for cancer, but an experimental link between defects in competition and tumorigenesis is elusive. In the thymus, T lymphocytes develop from precursors that are constantly replaced by bone-marrow-derived progenitors. Here we show that in mice this turnover is regulated by natural cell competition between 'young' bone-marrow-derived and 'old' thymus-resident progenitors that, although genetically identical, execute differential gene expression programs. Disruption of cell competition leads to progenitor self-renewal, upregulation of Hmga1, transformation, and T-cell acute lymphoblastic leukaemia (T-ALL) resembling the human disease in pathology, genomic lesions, leukaemia-associated transcripts, and activating mutations in Notch1. Hence, cell competition is a tumour suppressor mechanism in the thymus. Failure to select fit progenitors through cell competition may explain leukaemia in X-linked severe combined immune deficiency patients who showed thymus-autonomous T-cell development after therapy with gene-corrected autologous progenitors.