The precancerous lesion known as Barrett's oesophagus can evolve to oesophageal adenocarcinoma in decades-long processes of regenerative growth. Here we report the isolation and propagation of distinct, patient-matched stem cells of Barrett's, gastric and oesophageal epithelia that yield divergent tumour types following in vitro transformation and xenografting. Genomic analyses reveal a broad mutational spectrum unique to Barrett's stem cells that likely reflects their risk for oncogenesis. Remarkably, 25% of cases show no cancer-related genomic changes, suggesting that Barrett's initiates without driver mutations. Most cases, however, sustain patterns of deletions almost identical to adenocarcinoma though tumour-associated gene amplifications were absent. Notably, those suspected of low-grade dysplasia have p53 mutations or undergo amplifications of proto-oncogenes and receptor tyrosine kinases, implicating these events in lethal transitions. Our findings suggest paths for the initiation and progression of Barrett's and define a discrete stem cell underlying its regenerative growth whose eradication could prevent oesophageal adenocarcinoma.