The extent to which cells in normal tissues accumulate mutations throughout life is poorly understood. Some mutant cells expand into clones that can be detected by genome sequencing. We mapped mutant clones in normal esophageal epithelium from nine donors (age range, 20 to 75 years). Somatic mutations accumulated with age and were caused mainly by intrinsic mutational processes. We found strong positive selection of clones carrying mutations in 14 cancer genes, with tens to hundreds of clones per square centimeter. In middle-aged and elderly donors, clones with cancer-associated mutations covered much of the epithelium, with NOTCH1 and TP53 mutations affecting 12 to 80% and 2 to 37% of cells, respectively. Unexpectedly, the prevalence of NOTCH1 mutations in normal esophagus was several times higher than in esophageal cancers. These findings have implications for our understanding of cancer and aging.