Ab initio local-density functional studies of the adsorption of CO on the (100) surface of Rh have been performed. We show that although adsorption in the bridge site is always energetically more favorable than adsorption in either the on-top or the hollow sites, two different mechanisms can lead to a relatively high occupation of the on-top sites: (i) At higher coverage the interactions between the adsorbates stabilize a pseudohexagonal coincidence lattice with the experimentally observed p(4 (root)2 X (root)2) structure with a bridge/on-top ratio of 2:1 (all adsorbates being slightly shifted from their high-symmetry positions). (ii) At lower coverages there seems to be a contradiction between the energetic preference for bridge-site adsorption and the mixed top/bridge adsorption reported in the experiments. This could simply be dismissed as a failure of density-functional theory. However, we speculate about a possible way to reconcile the calculated potential energy surface and the experimental observations: At distances larger than 1.75 Angstrom from the surface (this is smaller than the equilibrium height for on-top adsorption), the interaction-energy with the on-top site is always larger by similar to 0.5 eV than with the bridge site. The on-top adsorbed molecule is metastable, because there is a barrier of 0.06 eV for migration to the bridge site and the reaction channel is very narrow. This leads to the observed mixed occupation of top and bridge sites at lower coverage (Theta less than or equal to 0.5).