Surveillance of Barrett’s oesophagus allows us to study the evolutionary dynamics of a human neoplasm over time. Here we use multicolour fluorescence in situ hybridization on brush cytology specimens, from two time points with a median interval of 37 months in 195 non-dysplastic Barrett's patients, and a third time point in a subset of 90 patients at a median interval of 36 months, to study clonal evolution at single-cell resolution. Baseline genetic diversity predicts progression and remains in a stable dynamic equilibrium over time. Clonal expansions are rare, being detected once every 36.8 patient years, and growing at an average rate of 1.58 cm[superscript 2] (95% CI: 0.09–4.06) per year, often involving the p16 locus. This suggests a lack of strong clonal selection in Barrett’s and that the malignant potential of ‘benign’ Barrett’s lesions is predetermined, with important implications for surveillance programs.