In this paper we study the translational and rotational diffusion of water trapped in up-to-50-μm-long (10, 10) SWCNTs of diameter d = (1.4 ± 0.1) nm by quasi-elastic neutron scattering (QENS), in the temperature interval from 300 to 10 K, with the purpose of observing the formation of the single-file water chain and nearly free-rotation of molecules. QENS is particularly suitable for this task as it essentially probes the hydrogen dynamics through the incoherent structure factor of hydrogen around the elastic region, giving information on the geometry of the diffusing system and the time scale of diffusion, ps in our case. The onset of sub-nanometer axial confinement in the (10, 10) SWCNTs should occur below 200 K, after the formation of a square-ice sheet rolled to form a channel coaxial to the nanotube. Therefore any peculiarity of water’s roto-translational dynamics below this temperature may become the signature of the emergence of the single-file structure and dynamics.