We present a combined experimental and theoretical study of the self-assembly of C60 molecules functionalized with long alkane chains on the (111) surface of silver. We find that the conformation of the functionalized C60 changes upon adsorption on Ag(111) and that the unit cell size in the self-assembled monolayer is determined by the interactions between the functional groups. We show that C60 molecules can be assembled in ordered 2D arrays with intermolecular distances much larger than those in compact C60 layers, and propose a novel way to control the surface pattern by appropriate chemical functionalization.