Single-file transport of water into carbon nanotubes is experimentally demonstrated for the first time through the splitting of the radial breathing mode (RBM) vibration in Raman spectra of bile salt solubilized tubes when both empty (closed) and water-filled (open-ended) tubes are present. D2O filling is observed for a wide range of diameters, d, down to very thin tubes [e.g., (5,3) tube, d=0.548 nm] for which only a single water molecule fits in the cross section of the internal nanotube channel. The shift in RBM frequency upon filling is found to display a very complex dependence on nanotube diameter and chirality, in support of a different yet well-defined ordering and orientation of water molecules at room temperature. Large shifts of the electronic transitions are also observed.