A century ago, Boveri proposed that cancer is caused by aneuploidy, an abnormal balance of chromosomes, because aneuploidy correlates with cancer and because experimental aneuploidy generates “pathological” phenotypes. Half a century later, when cancers were found to be nonclonal for aneuploidy, but clonal for somatic gene mutations, this hypothesis was abandoned. As a result, aneuploidy is now generally viewed as a consequence, and mutated genes as a cause of cancer. However, we have recently proposed a two-stage mechanism of carcinogenesis that resolves the discrepancy between clonal mutation and nonclonal karyotypes. The proposal is as follows: in stage 1, a carcinogen “initiates” carcinogenesis by generating a preneoplastic aneuploidy; in stage 2, aneuploidy causes asymmetric mitosis because it biases balance-sensitive spindle and chromosomal proteins and alters centrosomes both numerically and structurally (in proportion to the degree of aneuploidy). Therefore, the karyotype of an initiated cell evolves autocatalytically, generating ever-new chromosome combinations, including neoplastic ones. Accordingly, the heterogeneous karyotypes of “clonal” cancers are an inevitable consequence of the karyotypic instability of aneuploid cells. The notorious long latent periods, of months to decades, from carcinogen to carcinogenesis, would reflect the low probability of evolving by chance karyotypes that compete favorably with normal cells, in principle analagous to natural evolution. Here, we have confirmed experimentally five predictions of the aneuploidy hypothesis: (1) the carcinogens dimethylbenzanthracene and cytosine arabinoside induced aneuploidy in a fraction of treated Chinese hamster embryo cells; (2) aneuploidy preceded malignant transformation; (3) transformation of carcinogen-treated cells occurred only months after carcinogen treatment, i.e., autocatalytically; (4) preneoplastic aneuploidy segregated with malignant transformation in vitro and with 14 of 14 tumors in animals; and (5) karyotypes of tumors were heterogeneous. We conclude that, with the carcinogens studied, aneuploidy precedes cancer and is necessary for carcinogenesis.