The surface potential of the vapor-liquid interface of pure water is relevant to electrochemistry, solvation thermodynamics of ions, and interfacial reactivity. The chemistry of an ion near the vapor-liquid interface is influenced by the surface potential. Indirect determinations of the surface potential have been experimentally attempted many times, yet there has been little agreement as to its magnitude and sign (-1.1 to +0.5 V). We present the first computation of the surface potential of water using ab initio molecular dynamics and find a surface potential of -18 mV with a maximum interfacial electric field of +8.9 x 10(7) V/m, which are consistent with structural data from experiment. A comparison is made between our results and those from experiments and previous molecular simulations. The associated electric field can alter interfacial reactivity and transport, while the surface potential can be used to determine the "chemical" contribution to the real and electrochemical potentials for ion transport through the vapor-liquid interface.