Perhpas the most extreme examples of “Active OB stars" are the subset of high-mass X-ray binaries – consisting of an OB star plus compact companion – that have recently been observed by Fermi and ground-based Cerenkov telescopes like HESS to be sources of very high energy (VHE; up to 30 TeV!) γ-rays. This paper focuses on the prominent γ-ray source, LS5039, which consists of a massive O6.5V star in a 3.9-day-period, mildly elliptical (e ≈ 0.24) orbit with its companion, assumed here to be a black-hole or unmagnetized neutron star. Using 3-D SPH simulations of the Bondi-Hoyle accretion of the O-star wind onto the companion, we find that the orbital phase variation of the accretion follows very closely the simple Bondi-Hoyle-Lyttleton (BHL) rate for the local radius and wind speed. Moreover, a simple model, wherein intrinsic emission of γ-rays is assumed to track this accretion rate, reproduces quite well Fermi observations of the phase variation of γ-rays in the energy range 0.1-10 GeV. However for the VHE (0.1-30 TeV) radiation observed by the HESS Cerenkov telescope, it is important to account also for photon-photon interactions between the γ-rays and the stellar optical/UV radiation, which effectively attenuates much of the strong emission near periastron. When this is included, we find that this simple BHL accretion model also quite thus making it a strong alternative to the pulsar-wind-shock models commonly invoked to explain such VHE γ-ray emission in massive-star binaries.