PSR B1259-63 is a 47ms radio pulsar with a high spin-down luminosity which is in a close, highly eccentric 3.5-year orbit about a bright stellar companion. The binary system may be a detectable source of hard -rays produced by inverse Compton scattering of photons from the B2e star SS2883 by electrons and positrons in the pulsar wind. The star provides an enormous density of optical photons in the vicinity of the pulsar, particularly at epochs near periastron. We calculate the emission from the unshocked region of the pulsar wind, assuming that it terminates at a shock where it attains pressure balance with the companion's wind. The spectra and light curves for the inverse Compton emission from the shock-terminated wind are compared with those for an unterminated wind. If the pulsar's wind is weaker than that from the companion star, the termination of the wind decreases the inverse Compton flux, particularly near periastron. The termination shock geometry has the effect of decreasing the asymmetry of the -ray light curve around periastron, which arises because of the asymmetrical variation of the scattering angle.