Mammalian centromeres direct faithful genetic inheritance and are typically characterized by regions of highly repetitive and rapidly evolving DNA. We focused on a mouse species, Mus pahari, that we found has evolved to house centromere-specifying CENP-A nucleosomes at the nexus of a satellite repeat that we identified and term π-satellite (π-sat), a small number of recruitment sites for CENP-B, and short stretches of perfect telomere repeats. One M. pahari chromosome, however, houses a radically divergent centromere harboring ~6 Mbp of a homogenized π-sat-related repeat, π-satB, that contains >20,000 functional CENP-B boxes. There, CENP-B abundance drives accumulation of microtubule-binding components of the kinetochore, as well as a microtubule-destabilizing kinesin of the inner centromere. The balance of pro- and anti-microtubule-binding by the new centromere permits it to segregate during cell division with high fidelity alongside the older ones whose sequence creates a markedly different molecular composition.