A methodology for the successive regiospecific "clicking" together of three components in one pot via two triazole linkages is reported. The protocol utilizes copper(I)-mediated alkyne-azide cycloaddition reactions combined with a silver(I)-catalyzed TMS-alkyne deprotection under mild hydroalcoholic conditions. We exemplify the approach with peptide-based components to illustrate its compatibility with polyfunctionalized biomolecules. The method constitutes a promising tool for peptide ligation. We also provide a procedure for directly using TMS-alkynes as the cycloaddition partner in classical "click" chemistry.