Like blood neutrophils, dHL60 cells respond to a uniform concentration of attractant by polarizing in apparently random directions. How each cell chooses its own direction is unknown. We now find that an arrow drawn from the center of the nucleus of an unpolarized cell to its centrosome strongly predicts the subsequent direction of attractant-induced polarity: Of 60 cells that polarized in response to uniform f-Met-Leu-Phe (fMLP), 42 polarized to the left of this arrow, 6 polarized to the right, and 12 polarized directly toward or away from the centrosome. To investigate this directional bias we perturbed a regulatory pathway, downstream of Cdc42 and partitioning-defective 6 (Par6), which controls centrosome orientation relative to polarity of other cells. Dominant negative Par6 mutants block polarity altogether, as previously shown for disrupting Cdc42 activity. Cells remain able to polarize, but without directional bias, if their microtubules are disrupted with nocodazole, or they express mutant proteins that interfere with activities of PKCζ or dynein. Expressing constitutively active glycogen synthase kinase 3β (GSK3β) causes cells to polarize preferentially to the right. Distributions of most of these polarity regulators localize to the centrosome but show no left-right asymmetry before polarization. Together, these findings suggest that an intrinsically chiral structure, perhaps the centrosome, serves as a template for directing polarity in the absence of spatial cues. Such a template could help to determine left-right asymmetry and planar polarity in development.