The centromere is a defining feature of the eukaryotic chromosome, required for attachment to spindle microtubules and segregation to the poles at both mitosis and meiosis. The fundamental unit of centromere identity is the centromere-specific nucleosome, in which the centromeric histone 3 (cenH3) variant takes the place of H3. The structure of the cenH3 nucleosome has been the subject of controversy, as mutually exclusive models have been proposed, including conventional and unconventional left-handed octamers (octasomes), hexamers with non-histone protein constituents, and right-handed heterotypic tetramers (hemisomes). Hemisomes have been isolated from native centromeric chromatin, but traditional nucleosome assembly protocols have generally yielded partially unwrapped left-handed octameric nucleosomes. In budding yeast, topology analysis and high-resolution mapping has revealed that a single right-handed cenH3 hemisome occupies the ~80-bp Centromere DNA Element II (CDEII) of each chromosome. Overproduction of cenH3 leads to promiscuous low-level incorporation of octasome-sized particles throughout the yeast genome. We propose that the right-handed cenH3 hemisome is the universal unit of centromeric chromatin, and that the inherent instability of partially unwrapped left-handed cenH3 octamers is an adaptation to prevent formation of neocentromeres on chromosome arms.