Centromeres are defining features of eukaryotic chromosomes, providing sites of attachment for segregation during mitosis and meiosis. The fundamental unit of centromere structure is the centromeric nucleosome, which differs from the conventional nucleosome by the presence of a centromere-specific histone variant (CenH3) in place of canonical H3. We have shown that the CenH3 nucleosome core found in interphase Drosophila cells is a heterotypic tetramer, a "hemisome" consisting of one molecule each of CenH3, H4, H2A, and H2B, rather than the octamer of canonical histones that is found in bulk nucleosomes. The surprising discovery of hemisomes at centromeres calls for a reevaluation of evidence that has long been interpreted in terms of a more conventional nucleosome. We describe how the hemisome structure of centromeric nucleosomes can account for enigmatic properties of centromeres, including kinetochore accessibility, epigenetic inheritance, rapid turnover of misincorporated CenH3, and transcriptional quiescence of pericentric heterochromatin. Structural differences mediated by loop 1 are proposed to account for the formation of stable tetramers containing CenH3 rather than stable octamers containing H3. Asymmetric CenH3 hemisomes might interrupt the global condensation of octameric H3 arrays and present an asymmetric surface for kinetochore formation. We suggest that this simple mechanism for differentiation between centromeric and packaging nucleosomes evolved from an archaea-like ancestor at the dawn of eukaryotic evolution.