Functional nuclei and mitotic spindles are shown to assemble around DNA-coated beads incubated in Xenopus egg extracts. Bipolar spindles assemble in the absence of centrosomes and kinetochores, indicating that bipolarity is an intrinsic property of microtubules assembling around chromatin in a mitotic cytoplasm. Microtubules nucleated at dispersed sites with random polarity rearrange into two arrays of uniform polarity. Spindle-pole formation requires cytoplasmic dynein-dependent translocation of microtubules across one another. It is proposed that spindles form in the absence of centrosomes by motor-dependent sorting of microtubules according to their polarity.