Understanding the thermal conductivity of zinc oxide is of central importance in assessing its potential for a wide variety of applications in optoelectronics, power electronics and thermoelectric devices. Our inelastic neutron scattering studies of powder samples on the MARI spectrometer indicate the importance of phonon scattering and anharmonicity. We now propose to study the energy line shapes of the phonons by single-crystal inelastic neutron scattering using the LET spectrometer. We shall separate the contributions to the scattering from static defects and phonon-phonon scattering. Our results will be compared with first-principles density-functional theory. We expect to obtain a deeper understanding of anharmonicity in general, and the temperature dependence of the thermal conductivity of this technologically important material in particular.