Atomistic molecular dynamics simulations were used to study the structure and dynamics of water molecules inside an open-ended carbon nanotube placed in a bath of water molecules. The size of the nanotube permitted only a single file of water molecules within the nanotube. These water molecules exhibited a solid-like ordering at room temperature, which was quantified by calculating the pair correlation function. It was shown that, even for the longest observation times, the diffusion mode of the water molecules inside the nanotube was Fickian and not sub-diffusive. Also proposed was a one-dimensional random walk model for the diffusion of the water molecules inside the nanotube. Good agreement was found between the mean-square displacements calculated from the random walk model and from molecular dynamics simulations, thus confirming that the water molecules underwent normal mode diffusion inside the nanotube. This behavior was attributed to strong positional correlations that caused all of the water molecules inside the nanotube to move collectively as a single object. The average residence time of the water molecules inside the nanotube was shown to scale quadratically with the nanotube length. Strong Correlations and Fickian Water Diffusion in Narrow Carbon Nanotubes. B.Mukherjee, P.K.Maiti, C.Dasgupta, A.K.Sood: Journal of Chemical Physics, 2007, 126[12], 124704