Vega, the second brightest star in the northern hemisphere, serves as a primary spectral type standard. Although its spectrum is dominated by broad hydrogen lines, the narrower lines of the heavy elements suggested slow to moderate rotation, giving confidence that the ground-based calibration of its visible spectrum could be safely extrapolated into the ultraviolet and near-infrared (through atmosphere models), where it also serves as the primary photometric calibrator. But there have been problems: the star is too bright compared to its peers and it has unusually shaped absorption line profiles, leading some to suggest that it is a distorted, rapidly rotating star seen pole-on. Here we report optical interferometric observations that show that Vega has the asymmetric brightness distribution of the bright, slightly offset polar axis of a star rotating at 93 per cent of its breakup speed. In addition to explaining the unusual brightness and line shape peculiarities, this result leads to the prediction of an excess of near-infrared emission compared to the visible, in agreement with observations. The large temperature differences predicted across its surface call into question composition determinations, adding uncertainty to Vega's age and opening the possibility that its debris disk could be substantially older than previously thought.