Dendrimers containing 1,4-triazole linkages between each generation were grown divergently via the Click chemistry inspired Huisgen 1,3-dipolar cycloaddition reaction in the presence of a Cu(I) catalyst. The monomeric unit (1-propargylbenzene-3,5-dimethanol) contained the alkyne functionality, while the core (1,2-bis(2-azidoethoxy)ethane) and growing dendrimers presented the azide groups necessary for this type of Click reaction. The first generation dendrimer was also functionalized with alkyne termini to demonstrate an alternative pathway allowed by this chemistry. Synthesis and characterization, with infrared (IR), H-1 and C-13 NMR spectroscopies, high-resolution mass spectrometry, gel permeation chromatography (GPC), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA), are reported for these divergently grown dendrimers.