  Recent HESS observations show that microquasars in high-mass systems are
sources of VHE gamma-rays. A leptonic jet model for microquasar gamma-ray
emission is developed. Using the head-on approximation for the Compton cross
section and taking into account angular effects from the star's orbital motion,
we derive expressions to calculate the spectrum of gamma rays when nonthermal
jet electrons Compton-scatter photons of the stellar radiation field.
Calculations are presented for power-law distributions of nonthermal electrons
that are assumed to be isotropically distributed in the comoving jet frame, and
applied to $\gamma$-ray observations of LS 5039. We conclude that (1) the TeV
emission measured with HESS cannot result only from Compton-scattered stellar
radiation (CSSR), but could be synchrotron self-Compton (SSC) emission or a
combination of CSSR and SSC; (2) fitting both the HESS data and the EGRET data
associated with LS 5039 requires a very improbable leptonic model with a very
hard electron spectrum. Because the gamma rays would be variable in a leptonic
jet model, the data sets are unlikely to be representative of a simultaneously
measured gamma-ray spectrum. We therefore attribute EGRET gamma rays primarily
to CSSR emission, and HESS gamma rays to SSC emission. Detection of periodic
modulation of the TeV emission from LS 5039 would favor a leptonic SSC or
cascade hadron origin of the emission in the inner jet, whereas stochastic
variability alone would support a more extended leptonic model. The puzzle of
the EGRET gamma rays from LS 5039 will be quickly solved with GLAST. (Abridged)
