The physical properties of aqueous sodium chloride solutions have been studied theoretically, but so far no experimental diffusion data have been obtained under supercooled conditions. Here the results of H-1 NMR translational diffusion measurements of water in sodium chloride solutions in the temperature range 230 to 300 K and sodium chloride concentrations up to 4.2 mol/kg are presented. It was found that the diffusion data were well-described by the Vogel-Tamman-Fulcher relationship with concentration-dependent parameters D-0, B, and T-0. The results indicate that under supercooled conditions the influence of sodium chloride on water diffusion is much smaller than predicted by molecular dynamics simulations.