Barrett's esophagus is a pre-malignant lesion that can progress to esophageal adenocarcinoma. We perform a multi-omic analysis of pre-cancer samples from 146 patients with a range of outcomes, comprising 642 person years of follow-up. Whole genome sequencing reveals complex structural variants and LINE-1 retrotransposons, as well as known copy number changes, occurring even prior to dysplasia. The structural variant burden captures the most variance across the cohort and genomic profiles do not always match consensus clinical pathology dysplasia grades. Increasing structural variant burden is associated with: high levels of chromothripsis and breakage-fusion-bridge events; increased expression of genes related to cell cycle checkpoint, DNA repair and chromosomal instability; and epigenetic silencing of Wnt signalling and cell cycle genes. Timing analysis reveals molecular events triggering genomic instability with more clonal expansion in dysplastic samples. Overall genomic complexity occurs early in the Barrett's natural history and may inform the potential for cancer beyond the clinically discernible phenotype.