LiCoO2 is the prototypical cathode in lithium-ion batteries. Its crystal structure consists of Li+ and CoO2- layers that alternate along the hexagonal «0001»axis. It is well established that the ionic and electronic conduction are anisotropic, but little is known regarding the heat transport. We analyze the phonon dispersion and lifetimes using anharmonic lattice dynamics based on quantum-chemical force constants. Around room temperature, the thermal conductivity in the hexagonal ab plane of the layered cathode is ∼6 times higher than that along the c axis. An upper limit to the average thermal conductivity at T = 300 K of 38.5 W m-1 K-1 is set by short phonon lifetimes associated with anharmonic interactions within the octahedral face-sharing CoO2- network. Observations of conductivity <10 W m-1 K-1 can be understood by additional scattering channels including grain boundaries in polycrystalline samples. The impact on thermal processes in lithium-ion batteries is discussed.