Human pluripotent stem cells (hPSCs) frequently acquire chromosomal aberrations such as aneuploidy in culture. These aberrations progressively increase over time and may compromise the properties and clinical utility of the cells. The underlying mechanisms that drive initial genomic instability and its continued progression are largely unknown. Here, we show that aneuploid hPSCs undergo DNA replication stress, resulting in defective chromosome condensation and segregation. Aneuploid hPSCs show altered levels of actin cytoskeletal genes controlled by the transcription factor SRF, and overexpression of SRF rescues impaired chromosome condensation and segregation defects in aneuploid hPSCs. Furthermore, SRF downregulation in diploid hPSCs induces replication stress and perturbed condensation similar to that seen in aneuploid cells. Together, these results suggest that decreased SRF expression induces replicative stress and chromosomal condensation defects that underlie the ongoing chromosomal instability seen in aneuploid hPSCs. A similar mechanism may also operate during initiation of instability in diploid cells.