Small cholesterol clusters (Ch(n), 1 <= n <= 10) on water have been investigated by molecular dynamics simulations based on an empirical force field potential. The simulation results for clusters of increasing size highlight the processes that take place during the initial stages of cholesterol aggregation at low coverage. Our results show that at T = 280 K clusters form spontaneously out of a dilute two-dimensional (2D) vapor of cholesterol molecules, driven by entropy and potential energy. Up to it = 10, corresponding to 25% coverage for our simulation cell, cholesterol molecules lay flat on the water surface, forming fluid-like 2D aggregates, Within each island, the elongated cholesterol molecules align their longest axis along a common direction, anticipating the liquid-crystal character of bulk phases. With increasing cluster size, the adsorption energy per molecule quickly saturates to a value close to the limiting value for a full monolayer coverage. Cholesterol adsorption locally changes the electrostatic surface polarization of water, giving rise to an induced moment that tends to compensate the dipole of the adsorbed island. Computations for a single cholesterol molecule and dimer in bulk water are reported for a comparison. The absorption energy of both species in bulk water is larger than their adsorption energy at the water surface, thus pointing to entropy as the origin of the amphiphilic character of cholesterol.