Single crystalline gamma-Al2O3 layers have been successfully grown on silicon substrates by the metalorganic molecular beam epitaxy using aluminum alkoxide gas. Single crystalline gamma-Al2O3 layers are grown only on crystalline silicon substrates, while polycrystalline Al2O3 layers are grown on amorphous oxidized silicon surface. By x-ray photoemission spectroscopy measurements, the stoichiometry of the single crystalline layers were confirmed to be identical to Al2O3 bulk crystals and carbon contamination was not detected within the sensitivity of the measurements.