Kinetochores assemble on centromeric DNA and present arrays of proteins that attach directly to the dynamic ends of microtubules. Kinetochore proteins coordinate at the microtubule interface through oligomerization, but how oligomerization contributes to kinetochore function has remained unclear. Here, using a combination of biophysical assays and live-cell imaging, we find that oligomerization of the Dam1 complex is required for its ability to form microtubule attachments that are robust against tension in vitro and in vivo. An oligomerization-deficient Dam1 complex that retains wild-type microtubule binding activity is primarily defective in coupling to disassembling microtubule ends under mechanical loads applied by a laser trap in vitro. In cells, the oligomerization-deficient Dam1 complex is unable to support stable bipolar alignment of sister chromatids, indicating failure of kinetochore-microtubule attachments under tension. We propose that oligomerization is an essential and conserved feature of kinetochore components that is required for accurate chromosome segregation during mitosis.