Stochastic resonance in a fundamental single-electron circuit, i.e., a balanced pair of single-electron boxes, is observed and presented theoretically, where the signal-to-noise ratio (SNR) of the internal states stimulated by responding to a periodic subthreshold or suprathreshold input is enhanced by thermal agitation in tunneling junctions. Through extensive Monte-Carlo simulations, the peak SNR was determined as a function of temperature and input amplitudes. These results imply the possibility to design single-electron circuits that may "exploit" thermal noise, instead of employing conventional noise-suppression strategies.