Vesicles, which are droplets of a fluid encapsulated in a membrane, represent the basic structure of almost all life forms. The amphiphilic membrane that separates different domains acts as a tunable filter, selectively allowing the passage of chemical substances. The formation of these aggregates is subject of increasing interest, both experimental and theoretically, due to the fact that they can be used as drug carrier or even as artificial cells. In this paper, we report the first successful computer simulation of vesicle spontaneous formation obtained by performing extensive Monte Carlo calculations in a microscopic lattice model based on two-tailed amphiphilic chains surrounded by solvent molecules. The dynamical process of aggregation is also shown and some features of this process are discussed.