A cubane-like tetranuclear hydrosulfido complex of Cu(I), [Cu4(SH)4(PPh3)4] (1), has been synthesized by the reaction of Cu(NO3)2·3H2O, NaSCOPh, and Cu(PPh3)2NO3 and characterized structurally. Complex 1 represents the first example of crystallographically characterized μ3-SH-bridged cubanoid hydrosulfide. By direct reactions of [(PPh3)2Cu(NO3)] and NaSH, neutral hydrosulfide complexes [Cu(SH)(PPh3)2]·C6H6 (2), [Cu2(SH)2(PPh3)3] (3), and [Cu2(SH)2(PPh3)4] (4) have also been synthesized and structurally characterized. Complex 2 is monomeric with a terminal hydrosulfide ligand. The other two, 3 and 4, are μ2-SH-bridged unsymmetrical and symmetrical dinuclear complexes, respectively. In the symmetric one (4), both Cu(I) ions are tetrahedrally coordinated while in the unsymmetric one (3), one Cu(I) ion is tetrahedral and the other one has a trigonal-planar coordination geometry. The catalytic activity of a hydrosulfido complex in a "click" azide-alkyne cycloaddition reaction has been explored for the first time, and complex 1 is found to be an efficient catalyst for the regioselective synthesis of glycoconjugate triazoles.