Single-cell barcoding technologies enable genome sequencing of thousands of individual cells in parallel, but with extremely low sequencing coverage (<0.05×) per cell. While the total copy number of large multi-megabase segments can be derived from such data, important allele-specific mutations-such as copy-neutral loss of heterozygosity (LOH) in cancer-are missed. We introduce copy-number haplotype inference in single cells using evolutionary links (CHISEL), a method to infer allele- and haplotype-specific copy numbers in single cells and subpopulations of cells by aggregating sparse signal across hundreds or thousands of individual cells. We applied CHISEL to ten single-cell sequencing datasets of ~2,000 cells from two patients with breast cancer. We identified extensive allele-specific copy-number aberrations (CNAs) in these samples, including copy-neutral LOHs, whole-genome duplications (WGDs) and mirrored-subclonal CNAs. These allele-specific CNAs affect genomic regions containing well-known breast-cancer genes. We also refined the reconstruction of tumor evolution, timing allele-specific CNAs before and after WGDs, identifying low-frequency subpopulations distinguished by unique CNAs and uncovering evidence of convergent evolution.