  Very high energy (VHE) gamma-rays have recently been detected from the
Galactic black-hole candidate and microquasar LS 5039. A plausible site for the
production of these VHE gamma-rays is the region close to the mildly
relativistic outflow. However, at distances comparable to the binary
separation, the intense photon field of the stellar companion will lead to
substantial gamma-gamma absorption of VHE gamma-rays. If the system is viewed
at a substantial inclination (i > 0), this absorption feature will be modulated
on the orbital period of the binary as a result of a phase-dependent
stellar-radiation intensity and pair-production threshold. We apply our results
to LS 5039 and find that (1) gamma-gamma absorption effects will be substantial
if the photon production site is located at a distance from the central compact
object of the order of the binary separation (~ 2.5e12 cm) or less; (2) the
gamma-gamma absorption depth will be largest at a few hundred GeV, leading to a
characteristic absorption trough; (3) the gamma-gamma absorption feature will
be strongly modulated on the orbital period of the binary, characterized by a
spectral hardening accompanying periodic dips of the VHE gamma-ray flux; and
(4) gamma rays can escape virtually unabsorbed, even from within ~ 10^{12} cm,
when the star is located behind the production site as seen by the observer.
