Long range orientational order within C60 monolayers on Au(111) is observed with low-temperature scanning tunneling microscopy. A unit cell comprised of 49 molecules which adopt 11 different orientations is found. It can be divided in a faulted and an unfaulted half similar to the (7x7) reconstruction of Si(111). A model is proposed which shows how, through a Moiré-like effect, the substrate induces minute changes in the orientation of the C60 molecules. Intermolecular interactions are shown to play a major role in stabilizing the superlattice.