We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating A+1 / 2B(2) reaction on a square lattice. This stochastic resonance arises directly from the elementary reaction steps of the system without any external input. The lattice gas model is investigated by means of Monte Carlo simulations. It shows oscillation phenomena and mesoscopic pattern formation. Stochastic resonance arises when homogeneous nucleation of the individual lattice site states is considered. This nucleation is modeled as a weak noise process. As a result, synchronization of the kinetic oscillations is obtained. We show that all characteristics known from the research on stochastic resonance are obtained in our model. We also show that the model explains easily several phenomena observed in the experiment. Internal stochastic resonance may thus be an internal regulation mechanism of extreme adaptability.