Somatic mutations alter the genomes of a subset of an individual’s brain cells1–3, impacting gene regulation and contributing to disease processes4,5. Mosaic single nucleotide variants have been characterized with single-cell resolution in the brain2,3, but we have limited information about large-scale structural variation, including whole-chromosome duplication or loss1,6,7. We used a dataset of over 415,000 single-cell DNA methylation and chromatin conformation profiles across the adult mouse brain to identify aneuploid cells comprehensively. Whole-chromosome loss or duplication occurred in <1% of cells, with rates up to 1.8% in non-neuronal cell types, including oligodendrocyte precursors and pericytes. Among all aneuploidies, we observed a strong enrichment of trisomy on chromosome 16, which is syntenic with human chromosome 21 and constitutively trisomic in Down syndrome. Chromosome 16 trisomy occurred in multiple cell types and across brain regions, suggesting that nondisjunction is a recurrent feature of somatic variation in the brain.