The progression of precancerous lesions to malignancy is often accompanied by increasing complexity of chromosomal alterations but how these alterations arise is poorly understood. Here we perform haplotype-specific analysis of chromosomal copy-number evolution in the progression of Barrett's esophagus (BE) to esophageal adenocarcinoma (EAC) on multiregional whole-genome sequencing data of BE with dysplasia and microscopic EAC foci. We identify distinct patterns of copy-number evolution indicating multigenerational chromosomal instability that is initiated by cell division errors but propagated only after p53 loss. While abnormal mitosis, including whole-genome duplication, underlies chromosomal copy-number changes, segmental alterations display signatures of successive breakage-fusion-bridge cycles and chromothripsis of unstable dicentric chromosomes. Our analysis elucidates how multigenerational chromosomal instability generates copy-number variation in BE cells, precipitates complex alterations including DNA amplifications, and promotes their independent clonal expansion and transformation. In particular, we suggest sloping copy-number variation as a signature of ongoing chromosomal instability that precedes copy-number complexity. These findings suggest copy-number heterogeneity in advanced cancers originates from chromosomal instability in precancerous cells and such instability may be identified from the presence of sloping copy-number variation in bulk sequencing data.