Chromosome instability (CIN) is the most common form of genome instability and is a hallmark of cancer. CIN invariably leads to aneuploidy, a state of karyotype imbalance. Here, we show that aneuploidy can also trigger CIN. We found that aneuploid cells experience DNA replication stress in their first S-phase and precipitate in a state of continuous CIN. This generates a repertoire of genetically diverse cells with structural chromosomal abnormalities that can either continue proliferating or stop dividing. Cycling aneuploid cells display lower karyotype complexity compared to the arrested ones and increased expression of DNA repair signatures. Interestingly, the same signatures are upregulated in highly-proliferative cancer cells, which might enable them to proliferate despite the disadvantage conferred by aneuploidy-induced CIN. Altogether, our study reveals the short-term origins of CIN following aneuploidy and indicates the aneuploid state of cancer cells as a point mutation-independent source of genome instability, providing an explanation for aneuploidy occurrence in tumors.