In this paper we use density functional theory corrected for on-site Coulomb interactions (DFT+U) to study the adsorption of CO at La-doped ceria (111) and (110) surfaces. Doping of ceria with La is known to enhance oxidation of CO to CO(2) and this study investigates the atomic level details of this reaction. With La(3+) doping, an [La(3+)-O(-)] defect state with an oxygen hole is formed at both surfaces. The formation energy of an oxygen vacancy is reduced and vacancy formation results in the appearance of Ce(3+), instead of hole compensation. On the doped surfaces weak and strong adsorption of CO is found. In the former, the molecule remains intact. In the latter, the final adsorption species depends strongly on the surface and whether oxygen vacancies are present or not. On (111) a CO(2)-like species forms, while on the (110) surface, mono- or bidentate carbonates are present. La-doping of ceria surfaces shows enhanced reactivity over the undoped surfaces and we discuss the origin of the enhanced reactivity and the nature of the surface species upon CO adsorption.