The decomposition of N2O on a catalytic surface was simulated by the Monte Carlo method. The results show that both reaction rate and surface coverage oscillate with time. Fractal analysis of the time-series of surface coverages indicates that the oscillation observed has an attractor. The oscillation is chaotic in nature and the attractor is a fractal with a dimension about 3.5 when the rate constant k2 of the elementary step which produces O2 is large enough.