During vertebrate cell division, chromosomes oscillate with periods of smooth motion interrupted by abrupt reversals in direction. These oscillations must be spatially constrained in order to align and segregate chromosomes with high fidelity, but the molecular mechanism for this activity is uncertain. We report here that the human kinesin-8 Kif18A has a primary role in the control of chromosome oscillations. Kif18A accumulates as a gradient on kinetochore microtubules in a manner dependent on its motor activity. Quantitative analyses of kinetochore movements reveal that Kif18A reduces the amplitude of preanaphase oscillations and slows poleward movement during anaphase. Thus, the microtubule-depolymerizing kinesin Kif18A has the unexpected function of suppressing chromosome movements. Based on these findings, we propose a molecular model in which Kif18A regulates kinetochore microtubule dynamics to control mitotic chromosome positioning.