To determine if carbon-based materials can be used for hydrogen storage, we have studied hydrogen chemisorption in single-walled carbon nanotubes. Using atomic hydrogen as the hydrogenation agent, we demonstrated that maximal degree of nanotube hydrogenation depends on the nanotube diameter, and for the diameter values around 2.0 nm nanotube-hydrogen complexes with close to 100% hydrogenation exist and are stable at room temperature. This means that specific carbon nanotubes can have a hydrogen storage capacity of more than 7 wt % through the formation of reversible C-H bonds.