The interactions between the ions of the precious metals palladium, platinum, and rhodium with cerium dioxide, CeO2, have been studied using atomistic simulation techniques. We have investigated the structures and stabilities of the two low index surfaces of CeO2, (111) and (110); the results show that the (111) is more stable than the (110). We predict that metal ions such as Rh3+, Pd2+, and Pt2+ will segregate together with oxygen vacancies at the surface. The presence of noble metals thus modifies the surfaces of ceria which may be expected to influence considerably their catalytic activity.