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Doppler measurements from Keck exhibit a sinusoidal periodicity in the velocities of the G0 dwarf HD 209458, having a semiamplitude of 81 m s-1 and a period of 3.5239 days, which is indicative of a "51 Peg-like" planet with a minimum mass (M sin i) of 0.62 MJup and a semimajor axis of 0.046 AU. Follow-up photometry reveals a drop of 0.017 mag at the predicted time (within the errors) of transit by the companion based on the velocities. This is the first extrasolar planet observed to transit its star. The radius of the planet derived from the magnitude of the dimming is 1.42 RJup, which is consistent with models of irradiated Jupiter-mass planets. The transit implies that sin i > 0.993, leading to a true mass of 0.62 MJup for the planet. The resulting mean density of 0.27 g cm-3 implies that the companion is a gas giant.