Water is the most abundant volatile component in terrestrial basalts and is a significant constituent of the gases that escape from basaltic magmas. Knowledge of the diffusivity of water (and other volatiles) in basaltic melts is important for understanding the degassing of basaltic magma and for assessing the fractionation of volatiles during degassing. We report here measurements of water diffusivity in a basaltic liquid. The water concentration profiles through the samples, determined by Fourier-transform infrared spectroscopy, cannot be modelled adequately on the basis of a constant water diffusivity, but instead can be fitted by assuming that only molecular H2O is diffusing and that there is a local equilibrium between H2O molecules and OH groups. The concentration-dependent total water diffusivities in the basaltic melt at 1,300-1,500 degrees C are 30-50 times as large as those in rhyolitic melts, and are greater than the total CO2 diffusivity in basaltic melts, contrary to previous expectations. These results suggest that diffusive fractionation would increase the ratio of water to carbon dioxide in growing bubbles relative to equilibrium partitioning, and decrease the ratio in interface melts near an advancing anhydrous phenocryst.