We calculate the meteorology of the close-in transiting extrasolar planet HD 209458b using a global, three-dimensional atmospheric circulation model. Dynamics are driven by perpetual irradiation of one hemisphere of this tidally locked planet. The simulation predicts global temperature contrasts of ~500 K at the photosphere and the development of a steady superrotating jet. The jet extends from the equator to mid-latitudes and from the top model layer at 1 mbar down to 10 bars at the base of the heated region. Wind velocities near the equator exceed 4 km/s at 300 mbar. The hottest regions of the atmosphere are blown downstream from the substellar point by 60 degrees of longitude. We predict from these results a factor of ~2 ratio between the maximum and minimum observed radiation from the planet over a full orbital period, with peak infrared emission preceding the time of the secondary eclipse by ~14 hours.