We derive light curves for the hard gamma-ray emission, at energies up to s
everal TeV, expected from the unique pulsar/Bestar binary system PSR B1259-
63. This is the only known system in our galaxy in which a radio pulsar is
orbiting a main sequence star. We show that inverse Compton emission from t
he electrons and positrons in the shocked pulsar wind, scattering target ph
otons from the Be star, produces a flux of hard gamma-rays that should be a
bove the sensitivity threshold of present day atmospheric Cerenkov detector
s. Furthermore, we predict that the flux of hard gamma-rays produced via th
is mechanism has a characteristic variation with orbital phase that should
be observable, and which is not expected from any other mechanism, (C) 1999
Elsevier Science B.V.