We report the synthesis of superconducting MgB2 thin films grown in-situ by molecular beam epitaxy (MBE). Mg-rich fluxes are deposited with B-flux by electron beam evaporation onto c- and r-plane sapphire substrates. Deposition temperature is varied between 260 ∼ 320 °C. Base pressure of the MBE chamber is at low 10-10 Torr, rising to 10-8 Torr during deposition due mostly to the presence of hydrogen and nitrogen. Asgrown MgB2 films show superconducting transition at ∼ 34 K with ΔTc < 1 K. The films on c-plane sapphire substrates exhibit c-axis oriented peaks of MgB2, and full-width at half maximum of 3 degree in their rocking curves. Azimuthal phi-scan of the MgB2(101) peak shows 12-fold symmetric peaks, which is confirmed by selected area diffraction pattern in transmission electron microscopy (TEM). Plan-view TEM shows hexagonal-shaped grain growth with grain size of about 400 Å.