The adsorption of ethylene on a Si(100)-2 x 1 surface in an ultrahigh vacuum has been monitored at room temperature by use of real-time surface differential reflectance spectroscopy, which clearly demonstrated that the adsorption follows a two-stage process. About half a monolayer is obtained for 1 L, while the second stage is much slower, yielding the complete monolayer for an exposure of similar to 400 L. The kinetics over the full range has been successfully reproduced by a Monte Carlo calculation. The key point of this two-stage adsorption kinetic lies in the reduced adsorption probability (by a factor of several hundreds) on the Si dimers, neighbors of dimers which have already reacted, with respect to the adsorption probability on isolated dimers. This new kind of adsorption kinetics, due to a repulsion between already adsorbed molecules and additional molecules impinging on the surface, makes it a textbook case for a ``cooperative'' adsorption process.