Chromosome gains and losses are a frequent feature of human cancers. However, how these aberrations can outweigh the detrimental effects of aneuploidy remains unclear. An initial comparison of existing chromosomal instability (CIN) mouse models suggests that aneuploidy accumulates to low levels in these animals. We therefore developed a novel mouse model that enables unprecedented levels of chromosome missegregation in the adult animal. At the earliest stages of T-cell development, cells with random chromosome gains and/or losses are selected against, but CIN eventually results in the expansion of progenitors with clonal chromosomal imbalances. Clonal selection leads to the development of T-cell lymphomas with stereotypic karyotypes in which chromosome 15, containing the Myc oncogene, is gained with high prevalence. Expressing human MYC from chromosome 6 (MYCChr6) is sufficient to change the karyotype of these lymphomas to include universal chromosome 6 gains. Interestingly, while chromosome 15 is still gained in MYCChr6 tumors after genetic ablation of the endogenous Myc locus, this chromosome is not efficiently gained after deletion of one copy of Rad21, suggesting a synergistic effect of both MYC and RAD21 in driving chromosome 15 gains. Our results show that the initial detrimental effects of random missegregation are outbalanced by clonal selection, which is dictated by the chromosomal location and nature of certain genes and is sufficient to drive cancer with high prevalence.