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Carbon nanotubes (CNT) are known to provide a hydrophobic, confined environment for water where its structure and dynamics can be very different from those of bulk water. In particular, narrow CNTs of the type (6,6) allow only a single one-dimensional (1D) chain of water molecules inside them, thus providing an idealized scenario to study motion in 1D along water chains. In the present study, we have investigated structural and dynamic behavior of water and also of an excess proton and hydroxide ion in water-filled narrow CNTs by means of ab initio molecular dynamics and combined quantum-classical simulations. The main focus of the present work is on the molecular mechanism and kinetics of hydronium and hydroxide ion migration along 1D water chains of different lengths in confinement. It is found that the hydrogen-bonded structures of water and the excess proton and hydroxide ion in CNTs can be very …