First-principles molecular dynamics simulations have been carried out to investigate the structure, electronic properties, and proton conductivity of water confined inside single-walled carbon nanotubes. The simulations predict the formation of a strongly connected one-dimensional hydrogen-bonded water wire resulting in a net electric dipole moment directed along the nanotube axis. An excess proton injected into the water wire is found to be significantly stabilized, relative to the gas phase, due to the high polarizability of the carbon nanotube.