Growth of a single crystal was found in the first few oxide layers on GaAs(100) substrate, electron beam evaporated from a Ga5Gd3O12 source. Reflection high-energy electron diffraction and x-ray diffraction studies show that the thin oxide film is epitaxially grown on GaAs with the surface normal (110) and in-plane axis [001] parallel to (100) and [011] of GaAs, respectively, and the crystallographic structure is isomorphic to Mn2O3. The chemical composition of the oxide film was determined by x-ray photoelectron spectroscopy to be unequivocally pure Gd2O3. Based on Gibbs free energies of formation for all possible pairs in Ga, As, Gd, and O, a model is proposed to explain the epitaxy and the growth of single-domain Gd2O3 on GaAs.