The mechanisms for thermal (self) diffusion of Li ions in fully lithiated LiFePO4 have been investigated with spin polarized ab initio molecular dynamics calculations. The effect of electron correlation is taken into account with the GGA+U formalism. It was found that Li ion diffusion is not a continuous process but through a series of jumps from one site to another. A dominant process is the hopping between neighboring Li sites around the PO4 groups, which results in a zigzag pathway along the crystallographic b-axis. This observation is in agreement with a recent neutron diffraction experiment. A second process involves the collaborative movements of the Fe ions leading to the formation of antisite defects and promotes Li diffusion across the Li ion channels. The finding of the second mechanism demonstrates the benefit of ab initio molecular dynamics simulation in sampling diffusion pathways that may not be anticipated.