A computational study using the B3LYP/6-31G(d) level of theory shows that the chemisorptions of one and two hydrogen atoms on the external surface of (3,3), (4,4), (5,5), and (6,6) armchair single-walled carbon nanotubes (SWNTs) are exothermic processes. Our results clearly indicate that two hydrogen atoms favor binding at adjacent positions rather than at alternate carbon sites. This is different from the results reported on zigzag nanotubes (Yang et al. J. Phys. Chem. B 2006, 110, 6236). In general, the exothermicity of hydrogen chemisorption decreases as the diameter of the armchair nanotubes increases, which is in contrast to the observation for zigzag-type structures. The chemisorptions of one and two hydrogen atoms significantly alter the C−C bond lengths of the nanotube in the vicinity of hydrogen addition as a result of a change in hybridization of the carbon atom(s) at the chemisorption site(s) from sp2 to sp3. The effect of increasing the length of the SWNTs on the geometries and the reaction energies of hydrogen chemisorption has also been explored.