Herein, we investigate the reactivity of perfect and defective single-wall carbon nanotubes (SWCNTs) with the SH group using first principle periodic calculations. The presence of Stone-Wales (SW) defect sites significantly increases the reactivity of SWCNTs against the thiol group. The most reactive site for the addition of the SH radical is the single vacancy defect; the sulfur atom reconstructs the SWCNT framework and the hydrogen atom becomes attached to a carbon atom. The cluster model calculations performed for perfect SWCNTs confirmed a very low reactivity with the thiol group, even for the small diameter and metallic SWCNTs. The reaction between the perfect SWCNT and SH results thermodynamically unfavorable. The different reactivities observed for perfect and defective SWCNTs suggest that the SH group can be employed to perform a chemical labeling of the defect sites present in carbon nanotubes. The SH radical group is quite unique because, even though it has an unpaired electron, it does not react with sp (2) carbon frameworks, unless they have defects or curvature similar to C60. The results are discussed in terms of the recent experimental investigations about thiolated SWCNTs. We were able to explain the Transmission Electron Microscopy images of thiolated nanotubes and the lack of reactivity at the tips. Finally, we discuss a possible route to synthesize sulfur-doped SWCNTs using thiol groups and their electronic properties.