Human pluripotent stem cells offer a limitless source of cells for regenerative medicine. Neural derivatives of human embryonic stem cells (hESCs) are currently being used for cell therapy in 3 clinical trials. However, hESCs are prone to genomic instability, which could limit their clinical utility. Here, we report that neural differentiation of hESCs systematically produced a neural stem cell population that could be propagated for more than 50 passages without entering senescence; this was true for all 6 hESC lines tested. The apparent spontaneous loss of evolution toward normal senescence of somatic cells was associated with a jumping translocation of chromosome 1q. This chromosomal defect has previously been associated with hematologic malignancies and pediatric brain tumors with poor clinical outcome. Neural stem cells carrying the 1q defect implanted into the brains of rats failed to integrate and expand, whereas normal cells engrafted. Our results call for additional quality controls to be implemented to ensure genomic integrity not only of undifferentiated pluripotent stem cells, but also of hESC derivatives that form cell therapy end products, particularly neural lines.