The diffusion coefficient of Li+ ions (D(Li)) in the battery material LixCoO2 has been investigated by muon-spin relaxation (mu+SR). Based on experiments in zero and weak longitudinal fields at temperatures up to 400 K, we determined the fluctuation rate (nu) of the fields on the muons due to their interaction with the nuclear moments. Combined with susceptibility data and electrostatic potential calculations, clear Li+ ion diffusion was detected above approximately 150 K. The D(Li) estimated from nu was in very good agreement with predictions from first-principles calculations, and we present the mu+SR technique as an optimal probe to detect D(Li) for materials containing magnetic ions.