Unsymmetrical bisazides containing chelating and nonchelating azido groups undergo chemoselective three-component copper(I)-catalyzed azide-alkyne conjugation reactions with two different alkyne molecules. In conjunction with the reactivity gap between aromatic and aliphatic alkynes, a bistriazole molecule can be generated with excellent regioselectivity by mixing two alkynes and a bisazide in a single reaction container. This method is applicable in aqueous solutions at neutral pH, which may lend utilities in bioconjugation applications.