Single-cell genome sequencing has proven valuable for the detection of somatic variation, particularly in the context of tumor evolution. Current technologies suffer from high library construction costs, which restrict the number of cells that can be assessed and thus impose limitations on the ability to measure heterogeneity within a tissue. Here, we present single-cell combinatorial indexed sequencing (SCI-seq) as a means of simultaneously generating thousands of low-pass single-cell libraries for detection of somatic copy-number variants. We constructed libraries for 16,698 single cells from a combination of cultured cell lines, primate frontal cortex tissue and two human adenocarcinomas, and obtained a detailed assessment of subclonal variation within a pancreatic tumor.