We have investigated the aggregation into micelles of nonionic amphiphiles in water through Monte Carlo simulations of a very simple model system. Amphiphiles and water are modeled, respectively, as three-site and one-site molecules on a square lattice. The model presents characteristic properties of experimental micellization, namely, monomer vs amphiphile concentration with a plateau above a "critical" concentration (cmc) and a distribution of micelle sizes (polydispersity). Results of the numerical experiment were compared with predictions from statistical thermodynamic theory. Sample size and relaxation properties of the simulation have also been analyzed.