PSR B1259-63 is a 47 ms radio pulsar with a high spin-down luminosity which
is in a close, highly eccentric 3.5 yr orbit about a bright stellar compan
ion. The binary system may be a detectable source of hard gamma -rays produ
ced by inverse Compton scattering of photons from the B2e star SS2883 by el
ectrons and positrons in the pulsar wind. The star provides an enormous den
sity of optical photons in the vicinity of the pulsar. particularly at epoc
hs near periastron. We calculate the emission from the unshocked region of
the pulsar wind. assuming that it terminates at a shock where it attains pr
essure balance with the companion's wind. The spectra and light curves for
the inverse Compton emission from the shock-terminated wind are compared wi
th 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 gamma -ray light curve a
round periastron. which arises because of the asymmetrical variation of the
scattering angle.