This study introduces a novel single-cell genome sequencing method called Nuc-Seq, which utilizes G2/M nuclei to achieve high-coverage data with low error rates. The method was applied to sequence single normal and tumor nuclei from an estrogen-receptor positive (ER+) breast cancer and a triple-negative ductal carcinoma (TNBC). Single nuclei copy number profiling was also performed in parallel. The results show that aneuploid rearrangements occurred early in tumor evolution and remained stable, while point mutations evolved gradually, leading to extensive clonal diversity. Many of these mutations were found to occur at low frequencies (<10%) in the tumor mass. Mathematical modeling revealed that the TNBC had an increased mutation rate (13.3X) compared to the ER+ tumor. These findings have significant implications for understanding the diagnosis, treatment, and evolution of chemoresistance in breast cancer.This study introduces a novel single-cell genome sequencing method called Nuc-Seq, which utilizes G2/M nuclei to achieve high-coverage data with low error rates. The method was applied to sequence single normal and tumor nuclei from an estrogen-receptor positive (ER+) breast cancer and a triple-negative ductal carcinoma (TNBC). Single nuclei copy number profiling was also performed in parallel. The results show that aneuploid rearrangements occurred early in tumor evolution and remained stable, while point mutations evolved gradually, leading to extensive clonal diversity. Many of these mutations were found to occur at low frequencies (<10%) in the tumor mass. Mathematical modeling revealed that the TNBC had an increased mutation rate (13.3X) compared to the ER+ tumor. These findings have significant implications for understanding the diagnosis, treatment, and evolution of chemoresistance in breast cancer.