Density functional theory calculations predict that small clusters of Pd atoms, containing up to at least four atoms, are highly mobile on the MgO(100) surface with the tetramer having the largest diffusion rate at room temperature--larger than the monomer. Surface vacancies are found, however, to bind the larger clusters strongly enough to trap them. These are important considerations when analyzing the growth and sintering of metal islands on oxide surfaces, in particular, the role of point defects.