The Unfolded Protein Response (UPR) was discovered in budding yeast as a mechanism that allows cells to adapt to ER stress. While the Ire1 branch of this pathway is highly conserved, it is not thought to be important for cellular homeostasis in the absence of stress. Surprisingly, we found that removal of UPR activity led to pervasive aneuploidy in budding yeast cells, suggesting selective pressure resulting from UPR-deficiency. Aneuploid UPR-deficient cells grew better than euploid cells, but exhibited heightened general proteostatic stress, a hallmark of aneuploidy in wild-type cells. Modulation of key genes involved in ER proteostasis that were encoded on aneuploid chromosomes, could phenocopy the effects of aneuploidy, indicating that the reason cells require UPR activity to maintain euploidy is to counteract protein folding stress in the ER. In support of this model, aneuploidy in UPR-deficient cells can be prevented by expression of a UPR-independent general ER chaperone. Overall, our results indicate an unexpected role for the UPR in basal cell growth that is sufficiently important for cells to accept the costly trade-off of aneuploidy in the absence of UPR activity.