Cancer evolution involves cycles of genomic damage, epigenetic deregulation, and increased cellular proliferation that eventually culminate in the carcinoma phenotype. Early neoplasias, which are often found concurrently with carcinomas and are histologically distinguishable from normal breast tissue, are less advanced in phenotype than carcinomas and are thought to represent precursor stages. To elucidate their role in cancer evolution we performed comparative whole-genome sequencing of early neoplasias, matched normal tissue, and carcinomas from six patients, for a total of 31 samples. By using somatic mutations as lineage markers we built trees that relate the tissue samples within each patient. On the basis of these lineage trees we inferred the order, timing, and rates of genomic events. In four out of six cases, an early neoplasia and the carcinoma share a mutated common ancestor with recurring aneuploidies, and in all six cases evolution accelerated in the carcinoma lineage. Transition spectra of somatic mutations are stable and consistent across cases, suggesting that accumulation of somatic mutations is a result of increased ancestral cell division rather than specific mutational mechanisms. In contrast to highly advanced tumors that are the focus of much of the current cancer genome sequencing, neither the early neoplasia genomes nor the carcinomas are enriched with potentially functional somatic point mutations. Aneuploidies that occur in common ancestors of neoplastic and tumor cells are the earliest events that affect a large number of genes and may predispose breast tissue to eventual development of invasive carcinoma.