Ideal discrete energy levels in synthesized Au nanoparticles (6.2 ± 0.8 nm) for a chemically assembled single-electron transistor (SET) are demonstrated at 300 mK. The spatial structure of the double-gate SET is determined by two gate and drain voltages dependence of the stability diagram, and electron transport to the Coulomb box of a single, nearby Coulomb island of Au nanoparticles is detected by the SET. The SET exhibits discrete energy levels, and the excited energy level spacing of the Coulomb island is evaluated as 0.73 meV, which well corresponds to the expected theoretical value. The discrete energy levels show magnetic field evolution with the Zeeman effect and dependence on the odd-even electron number of a single Au nanoparticle.