Cancer is considered an outcome of decades-long clonal evolution fueled by acquisition of somatic genomic abnormalities (SGAs). Non-steroidal anti-inflammatory drugs (NSAIDs) have been shown to reduce cancer risk, including risk of progression from Barrett's esophagus (BE) to esophageal adenocarcinoma (EA). However, the cancer chemopreventive mechanisms of NSAIDs are not fully understood. We hypothesized that NSAIDs modulate clonal evolution by reducing SGA acquisition rate. We evaluated thirteen individuals with BE. Eleven had not used NSAIDs for 6.2±3.5 (mean±standard deviation) years and then began using NSAIDs for 5.6±2.7 years, whereas two had used NSAIDs for 3.3±1.4 years and then discontinued use for 7.9±0.7 years. 161 BE biopsies, collected at 5–8 time points over 6.4–19 years, were analyzed using 1Million-SNP arrays to detect SGAs. Even in the earliest biopsies there were many SGAs (284±246 in 10/13 and 1442±560 in 3/13 individuals) and in most individuals the number of SGAs changed little over time, with both increases and decreases in SGAs detected. The estimated SGA rate was 7.8 per genome per year (95% support interval [SI], 7.1–8.6) off-NSAIDs and 0.6 (95% SI 0.3–1.5) on-NSAIDs. Twelve individuals did not progress to EA. In ten we detected 279±86 SGAs affecting 53±30 Mb of the genome per biopsy per time point and in two we detected 1,463±375 SGAs affecting 180±100 Mb. In one individual who progressed to EA we detected a clone having 2,291±78 SGAs affecting 588±18 Mb of the genome at three time points in the last three of 11.4 years of follow-up. NSAIDs were associated with reduced rate of acquisition of SGAs in eleven of thirteen individuals. Barrett's cells maintained relative equilibrium level of SGAs over time with occasional punctuations by expansion of clones having massive amount of SGAs