Materials with the olivine LixMPO4 structure form an important class of rechargeable battery cathodes. Using first-principles methods, activation barriers to Li ion motion are calculated and an estimate for Li diffusion constants, in the absence of electrical conductivity constraints, is made. Materials with M=Mn, Fe, Co, Ni are considered. Li diffuses through one-dimensional channels with high energy barriers to cross between the channels. Without electrical conductivity limitations the intrinsic Li diffusivity is high. (C) 2003 The Electrochemical Society.