The C-l carbon of the dihydrated sodium salt of hydrogen bis(4-nitrophenoxide) gives rise to a single, unsplit, unbroadened signal in the solid-state, magic-angle spinning C-13 NMR spectrum of a crystalline powder even at 12 K. The results of rotational-echo, double-resonance C-13 NMR experiments with H-2 dephasing for the single C-13-1 resonance, when combined with the observation of a large isotropic J coupling for this carbon and other information, led to the conclusion that the bridging hydrogen (or deuterium) oscillates rapidly between the two basic oxygen sites. The average lifetime of a proton in one of these sites must be <10(-4) s even at 12 K. The bridge hydrogen therefore occupies a low-barrier, double-well potential with a ground vibrational level below the central maximum. These conclusions are consistent with the crystal structure, in which the two phenoxide units are related by a rotational axis of symmetry, and the oxygen-oxygen distance is only 2.452 Angstrom. The conclusions are also consistent with the unusual isotropic chemical shift of the bridge deuterium of 16.8 ppm relative to external tetramethylsilane. An apparent isotopic fractionation factor of 0.63 has been determined for the bridge hydrogen in the dihydrated sodium salt. This value appears to be too high in view of the other characteristics of the bridge hydrogen in the crystalline solid, which suggests that the solid was not in isotopic equilibrium with the solvent from which it was precipitated.