Epitaxial growth of single-crystal gadolinium oxide dielectric thin films on gallium arsenide is reported. The gadolinium oxide film has a cubic structure isomorphic to manganese oxide and is (110)-oriented in single domain on the (100) gallium arsenide surface. The gadolinium oxide film has a dielectric constant of approximately 10, with low leakage current densities of about 10(-9) to 10(-10) amperes per square centimeter at zero bias. Typical breakdown field is 4 megavolts per centimeter for an oxide film 185 angstroms thick and 10 megavolts per centimeter for an oxide 45 angstroms thick. Both accumulation and inversion layers were observed in the gadolinium oxide-gallium arsenide metal oxide semiconductor diodes, using capacitance-voltage measurements. The ability to grow thin single-crystal oxide films on gallium arsenide with a low interfacial density of states has great potential impact on the electronic industry of compound semiconductors.