Abstract Background Chromosome instability leads to aneuploidy, a state in which cells have abnormal numbers of chromosomes, and is found in two out of three cancers. In a chromosomal instable p53 deficient mouse model with accelerated lymphomagenesis, we previously observed whole chromosome copy number changes affecting all lymphoma cells. This suggests that chromosome instability is somehow suppressed in the aneuploid lymphomas or that selection for frequently lost/gained chromosomes out-competes the CIN-imposed mis-segregation. Results To distinguish between these explanations and to examine karyotype dynamics in chromosome instable lymphoma, we use a newly developed single-cell whole genome sequencing (scWGS) platform that provides a complete and unbiased overview of copy number variations (CNV) in individual cells. To analyse these scWGS data, we develop AneuFinder, which allows annotation of copy number changes in a fully automated fashion and quantification of CNV heterogeneity between cells. Single-cell sequencing and AneuFinder analysis reveals high levels of copy number heterogeneity in chromosome instability-driven murine T-cell lymphoma samples, indicating ongoing chromosome instability. Application of this technology to human B cell leukaemias reveals different levels of karyotype heterogeneity in these cancers. Conclusion Our data show that even though aneuploid tumours select for particular and recurring chromosome combinations, single-cell analysis using AneuFinder reveals copy number heterogeneity. This suggests ongoing chromosome instability that other platforms fail to detect. As chromosome instability might drive tumour evolution, karyotype analysis using single-cell sequencing technology could become an essential tool for cancer treatment stratification.