The formation of epitaxial crystalline islands of C60 on both the Si(111)7 X 7 and Si(111)square-root 3 X square-root 3-B surfaces is shown to follow an initial growth of a disordered layer and islands. This process is associated with a disordered-to-ordered interface transition at a critical coverage of three monolayers. Such a transition is driven and stabilized by the interlayer molecular couplings owing to the short range van der Waals interactions between the C60 molecules.