The addition of low levels of rare-earth or noble metals alters the redox properties and hydrocarbon oxidation activity of ceria-based materials, which has implications for their use in Solid Oxide Fuel Cell anodes. The surface structure of the metal-CeO2 catalyst is a function of operating conditions, yet the impact of the surface structure on hydrocarbon oxidation activity remains unresolved. We use density functional theory (DFT+U) to examine the energetics of methane oxidation and oxygen vacancy formation over ceria surfaces with the addition of transition metals. The structure, stability, and oxidation activity of single noble metal atoms on ceria is explored by considering the thermodynamics of Pd atom interaction with single crystal CeO2 surfaces. At certain pressure, temperature and potential ranges, mixed palladium-ceria oxide formation is favorable relative to single adsorbed Pd atoms or PdOx species. Oxidation over pure ceria is limited by high activation barriers to C-H dissociation, whereas kinetics over the Pd-ceria are limited by re-oxidation of oxygen vacancies. The catalytic activity of oxide anode electrocatalysts for direct hydrocarbon use in SOFCs may be optimized by design of a mixed oxide properly chosen for the anode operating conditions.