Faithful chromosome segregation requires the combined activities of the microtubule-based mitotic spindle and the multiple proteins that form mitotic kinetochores. Here, we show that the fission yeast mitotic mutant, tsm1-512, is an allele of the tubulin folding chaperone, cofactor D. Chromosome segregation in this and in an additional cofactor D mutant depends on growth conditions that are monitored specifically by the mitotic checkpoint proteins Mad1, 2, 3 and Bub3. The temperature-sensitive mutants we have used disrupt the function of cofactor D to different extents, but both strains form a mitotic spindle in which the poles separate in anaphase. However, chromosome segregation is often unequal, apparently due to a defect in kinetochore-microtubule interactions. Mutations in cofactor D render cells particularly sensitive to the expression levels of a CENP-B-like protein, Abp1p, which works as an allele-specific, high-copy suppressor of cofactor D. This and other genetic interactions between cofactor D mutants and specific kinetochore and spindle components suggest their critical role in establishing the normal kinetochore-microtubule interface.