Based on a mesoscopic stochastic model, we have studied the effect of particle size in the catalytic oxidation of CO on nanometer-sized palladium particles, using chemical Langevin equations. The reaction rate oscillations are of a stochastic nature, because of considerable internal noise in such mesoscopic systems. The performance of the stochastic oscillations undergoes a maximum with the variation of the particle size at a given CO partial pressure, which demonstrates the occurrence of particle size resonance. Such a phenomenon is robust to the change of CO pressure, except for some quantitative discrepancies. These results imply that there exists an optimal particle size for the CO oxidation over nanometer-sized supported palladium particles.