A new O induced structure on Rh(111) displaying a (2 sqaureroot[3] x 2sqaureroot[3])R30 degrees periodicity with an oxygen coverage of 2/3 has been studied by high resolution core level spectroscopy, scanning tunneling microscopy, and density functional theory. Although O favors fcc hollow sites in all other known phases, it occupies both fcc and hcp sites in this structure, which cannot be explained by pairwise adsorbate repulsion only. Both the (2sqaureroot[3] x 2sqaureroot[3])R30 degrees and (2 x 2)-3O structures also exemplify that density-of-states contrast can lead to oxygen adatoms appearing as protrusions in scanning tunneling microscopy images.