Chromosome segregation in metazoans requires the alignment of sister kinetochores on the metaphase plate. During chromosome alignment, bioriented kinetochores move chromosomes by regulating the plus-end dynamics of the attached microtubules. The bundles of kinetochore-bound microtubules alternate between growth and shrinkage, leading to regular oscillations along the spindle axis. However, the molecular mechanisms that coordinate microtubule plus-end dynamics remain unknown. Here we show that centromere protein (CENP)-H, a subunit of the CENP-A nucleosome-associated and CENP-A distal complexes (CENP-A NAC/CAD), is essential for this coordination, because kinetochores lacking CENP-H establish bioriented attachments but fail to generate regular oscillations, as a result of an uncontrolled rate of microtubule plus-end turnover. These alterations lead to rapid erratic movements that disrupt metaphase plate organization. We also show that the abundance of the CENP-A NAC/CAD subunits CENP-H and CENP-I dynamically change on individual sister kinetochores in vivo, because they preferentially bind the sister kinetochore attached to growing microtubules, and that one other subunit, CENP-Q, binds microtubules in vitro. We therefore propose that CENP-A NAC/CAD is a direct regulator of kinetochore-microtubule dynamics, which physically links centromeric DNA to microtubule plus ends.