The discovery that somatic cells are reprogrammable to pluripotency by ectopic expression of a small subset of transcription factors has created great potential for the development of broadly applicable stem-cell-based therapies. One of the concerns regarding the safe use of induced pluripotent stem cells (iPSCs) in therapeutic applications is loss of genomic integrity, a hallmark of various human conditions and diseases, including cancer. Structural chromosome defects such as short telomeres and double-strand breaks are known to limit reprogramming of somatic cells into iPSCs, but whether defects that cause whole-chromosome instability (W-CIN) preclude reprogramming is unknown. Here we demonstrate, using aneuploidy-prone mouse embryonic fibroblasts (MEFs) in which chromosome missegregation is driven by BubR1 or RanBP2 insufficiency, that W-CIN is not a barrier to reprogramming. Unexpectedly, the two W-CIN defects had contrasting effects on iPSC genomic integrity, with BubR1 hypomorphic MEFs almost exclusively yielding aneuploid iPSC clones and RanBP2 hypomorphic MEFs karyotypically normal iPSC clones. Moreover, BubR1-insufficient iPSC clones were karyotypically unstable, whereas RanBP2-insufficient iPSC clones were rather stable. These findings suggest that aneuploid cells can be selected for or against during reprogramming depending on the W-CIN gene defect and present the novel concept that somatic cell W-CIN can be concealed in the pluripotent state. Thus, karyotypic analysis of somatic cells of origin in addition to iPSC lines is necessary for safe application of reprogramming technology.