ZnO-based organic/inorganic hybrid semiconductor compounds have been grown heteroepitaxially in one step at low temperature by a simple electrochemical method from an oxygenated zinc chloride aqueous solution. The substrate is GaN(0001) single crystals, and the organic compound is a dye, eosin Y, dissolved in the deposition bath. The epitaxial growth of the hybrid is observed between -1.2 and -1.5 V versus the mercurous sulfate electrode. The deposit morphology changes dramatically with the deposition potential in relation to the redox state of eosin Y during the deposition. Various experiments show that an open nanostructured film is formed when the dye is co-deposited in its reduced form, while a compact structure is formed when the dye is included in its oxidized form. The structural relationship with single crystalline GaN and the quality of epitaxial ZnO have been studied by reflection high-energy electron diffraction (RHEED) and five-circle X-ray diffraction techniques. The polycrystalline phase content is negligible. The in-plane misorientation increases significantly with the dye loading, that is, with negative potential. This is interpreted in terms of detrimental effect of the presence of dye on the ZnO structural unit matching with the GaN surface. The epitaxial nature of these hybrid organic/inorganic films opens new perspectives for high quality device applications.