Less than half of human zygotes survive to live birth, primarily due to aneuploidies of meiotic or mitotic origin. Mitotic errors lead to chromosomal mosaicism, defined by multiple cell lineages with distinct chromosome complements. The incidence and fitness consequences of chromosomal mosaicism in human embryos remain controversial, with most previous studies based on bulk DNA assays or comparisons of multiple biopsies of a few embryonic cells. Single-cell genomic data provide an opportunity to quantify mosaicism on an embryo-wide scale. To this end, we extended an approach to infer aneuploidies based on chromosome dosage-associated changes in gene expression by integrating signatures of allelic imbalance. We applied this method to published single-cell RNA sequencing data from 74 disaggregated human embryos, spanning the morula to blastocyst stages. Our analysis revealed widespread mosaic aneuploidies across preimplantation development, with 59 of 74 (80%) embryos harboring at least one aneuploid cell (1% FDR). By clustering copy number calls, we reconstructed histories of chromosome mis-segregation, distinguishing meiotic and early mitotic errors from those occurring after lineage differentiation. We observed no significant enrichment of aneuploid cells in the trophectoderm compared to the inner cell mass, though we do detect such an enrichment in published data from later post-implantation stages. Finally, we observed that aneuploid cells exhibit upregulation of immune response genes, as well as downregulation of genes involved in proliferation, metabolism, and protein processing, consistent with stress responses previously documented in other stages and systems. Together, our work provides a high-resolution view of aneuploidy in preimplantation embryos and supports the conclusion that low-level mosaicism is a common feature of early human development.