PSR J2032+4127 is a γ-ray and radio-emitting pulsar which has been regarded as a young luminous isolated neutron star. However, its recent spin-down rate has extraordinarily increased by a factor of 2. We present evidence that this is due to its motion as a member of a highly-eccentric binary system with an ˜15-M⊙ Be star, MT91 213. Timing observations show that, not only are the positions of the two stars coincident within 0.4 arcsec, but timing models of binary motion of the pulsar fit the data much better than a model of a young isolated pulsar. MT91 213, and hence the pulsar, lie in the Cyg OB2 stellar association, which is at a distance of only 1.4-1.7 kpc. The pulsar is currently on the near side of, and accelerating towards, the Be star, with an orbital period of 20-30 yr. The next periastron is well constrained to occur in early 2018, providing an opportunity to observe enhanced high-energy emission as seen in other Be-star binary systems.