Human pluripotent stem cells (hPSCs) maintain diploid populations for generations despite a persistently high rate of mitotic errors that cause aneuploidy, or chromosome imbalances. Consequently, to maintain genome stability, aneuploidy must inhibit hPSC proliferation, but the mechanisms are unknown. Here, we surprisingly find that homogeneous aneuploid populations of hPSCs proliferate unlike aneuploid non-transformed somatic cells. Instead, in mosaic populations, cell non-autonomous competition between neighboring diploid and aneuploid hPSCs eliminates less fit aneuploid cells. Aneuploid hPSCs with lower Myc or higher p53 levels relative to diploid neighbors are outcompeted but conversely gain a selective advantage when Myc and p53 relative abundance switches. Thus, although hPSCs frequently missegregate chromosomes and inherently tolerate aneuploidy, Myc- and p53-driven cell competition preserves their genome integrity. These findings have important implications for the use of hPSCs in regenerative medicine and for how diploid human embryos are established despite the prevalence of aneuploidy during early development.