The evolution of binary systems is governed by their orbital properties and the stellar density of the local environment. Studies of neutron stars in binary star systems offer unique insights into both these issues. In an Arecibo survey of the Galactic disk, we have found PSR J1903+0327, a radio emitting neutron star (a "pulsar") with a 2.15 ms rotation period, in a 95-day orbit around a massive companion. Observations in the infra-red suggests that the companion may be a main-sequence star. Theories requiring an origin in the Galactic disk cannot account for the extraordinarily high orbital eccentricity observed (0.44) or a main-sequence companion of a pulsar that has spin properties suggesting a prolonged accretion history. The most likely formation mechanism is an exchange interaction in a globular star cluster. This requires that the binary was either ejected from its parent globular cluster as a result of a three-body interaction, or that that cluster was disrupted by repeated passages through the disk of the Milky Way.