During aging, progenitor cells acquire mutations, which may generate clones that colonize the surrounding tissue. By middle age, normal human tissues, including the esophageal epithelium (EE), become a patchwork of mutant clones. Despite their relevance for understanding aging and cancer, the processes that underpin mutational selection in normal tissues remain poorly understood. Here, we investigated this issue in the esophageal epithelium of mutagen-treated mice. Deep sequencing identified numerous mutant clones with multiple genes under positive selection, including Notch1, Notch2 and Trp53, which are also selected in human esophageal epithelium. Transgenic lineage tracing revealed strong clonal competition that evolved over time. Clone dynamics were consistent with a simple model in which the proliferative advantage conferred by positively selected mutations depends on the nature of the neighboring cells. When clones with similar competitive fitness collide, mutant cell fate reverts towards homeostasis, a constraint that explains how selection operates in normal-appearing epithelium. Deep sequencing and lineage tracing analysis of esophageal epithelium of mutagen-treated aging mice leads to a model in which the proliferative advantage of positively selected mutations depends on the competitive fitness of neighboring cells.