We report on the epitaxial deposition of magnesium oxide films with [111] crystallographic orientation on (0002) GaN by molecular beam epitaxy. Specifically, we use an adsorption controlled growth mechanism to initiate the growth process. Electron diffraction shows a spotty intense pattern without intensity fluctuations during growth and evidence of in-plane twinning. X-ray diffraction reveals the films to be epitaxial with full width at half maximum values of 0.3°, 0.5°, and 1° in 2θ, ϕ, and χ circles, respectively. Wet etching of the GaN surface with a HCl:HF mixture prior to growth is critical for achieving high crystalline quality. Epitaxial growth is observed between room temperature and 650°C, with negligible changes in crystalline quality with increased temperature. Atomic force microscopy analysis shows grainy surfaces with feature sizes near 10nm and rms roughness values of 1.4Å over 1μm2 areas. X-ray diffraction analysis suggests MgO film stability up to 850°C in ex situ air annealing.