THE rate at which tidal energy is dissipated in the solid Earth can constrain the anelastic properties of the Earth at frequencies much lower than those accessible with seismology. The dissipative properties of a system are usually expressed as a 'quality factor', Q; estimates1-7 of the semi-diurnal solid-Earth Q range from 90 to 500. But observational constraints on this quantity are difficult to obtain, because dissipation by the body tide is masked by the much greater dissipation that occurs in the oceans8,9. Here we show that recent accurate measurements of the ocean tide obtained by the Topex/Poseidon satellite altimeter10, combined with nearly two decades of laser tracking of satellite orbit perturbations11 (which are sensitive to the total planetary dissipation rate), permit an estimate of the solid-Earth dissipation rate at semi-diurnal period. We find that the body tide lags the principal lunar tidal potential by 0.16+/-0.09°, implying a dissipation rate of 83+/-45 gigawatts and a solid-Earth Q of 370 at a period of 12.4 hours. The observed lag agrees well with Zschau's 'most probable' lag1 of 0.21° (deduced from observations of the Chandler wobble), and favours the higher values of Q estimated theoretically.