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 stars 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)
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