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The discovery of the first known radio pulsar with a massive, nondegenerate companion is reported. PSR 1259-63, found during a large-scale high-frequency survey of the southern Galactic plane, has a period of 47 ms and a pulse profile similar to that of the Crab pulsar. Observations using the Parkes radio telescope at frequencies around 660 and 1520 MHz over the period 1989 November to 1991 September show that the pulsar is in a highly eccentric orbit around a massive companion. Near periastron, the pulsar is eclipsed, presumably by a wind from the companion star. On the basis of astrometric measurements, the companion has been optically identified as a 10th magnitude Be star, SS 2883. This unique system forms a link between Be X-ray binary systems and recycled pulsars.