Microwave irradiation promoted the intramolecular cycloaddition of 2-azidoacetamides derived from α-chiral propargylic amines, affording 1,4,5-trisubstituted triazoles 4 bearing a chiral aminomethyl side chain at C5. In contrast, for the same substrates 3a-k, Cu(I)-NHC complexes catalyzed the intermolecular cycloaddition in an unexpected desilylative fashion, leading to 1,4-disubstituted triazoles 5. This demonstrates that 1-silyl alkynes can be employed as substrates for CuAAC with a suitable coupling partner.