We report on the preparation of epitaxial MgO film on GaAs(001) substrates by molecular beam epitaxy at growth temperature of 20–200 °C. Reflection high energy electron diffraction, x-ray diffraction, and high resolution transmission electron microscopy reveal the growth of ordered crystalline cubic MgO(001) film at ∼200 °C with MgO(001)[100] || GaAs(001)[100] and a 4 : 3 lattice registry. The surface of the MgO films, characterized by atomic force microscopy, exhibits a root mean square roughness of only 0.5 nm. In situ stress measurements reveal tensile stress as low as 1.7 GPa for a growth temperature of 200 °C in good agreement with the calculated residual misfit strain.