Thermal expansion of solids arises from anharmonic lattice dynamics. The contrasting phenomenon of negative thermal expansion (NTE)-where expansion occurs on cooling rather than heating -was discovered(1) in ZrW2O8 in 1968. Recently, this material has attracted interest in the context of NTE for several reasons : the magnitude of the effect is relatively large (-9 p.p.m. K-1); the temperature range over which NTE occurs is also large (from close to absolute zero up to the decomposition temperature of about 1,050 K); and the NTE effect is isotropic(2), evidenced by the fact that ZrW2O8 remains cubic at all temperatures. These characteristics make ZrW2O8 an important system in which to study unusual lattice dynamics of this type, and potentially well suited for application in composite materials with an engineered thermal expansion coefficient(3). Here we report neutron-scattering measurements of ZrW2O8 that allow us to investigate its phonon spectrum, and hence determine the energy scale for the lattice motions governing NTE. We find that NTE can be modelled by several lo cv-energy phonon modes, suggesting that the effect arises from the unusual crystal structure of ZrW2O8, which supports highly anharmonic vibrational modes.