Living anionic copolymerizations of silyl-protected propargyl acrylate (TMS-PA) and 6-chlorohexyl methacrylate (CHMA) were conducted in the presence of ethylaluminum bis(2,6-di-tert-butylphenoxide) [EtAl(ODBP)2], a bulky aluminum Lewis acid, in toluene at ź60 °C. The polymerization proceeded in a monomer-selective manner, where the acrylate, TMS-PA, was selectively activated by EtAl(ODBP)2 and polymerized preferentially over to the methacrylate, CHMA, and the polymerization of CHMA followed after the complete consumption of TMS-PA to afford a block copolymer with narrow molecular weight distribution. The blocky sequence was confirmed with 1H NMR spectrum, while the peak shift of size exclusion chromatograms (SECs) from low to high molecular weights as well as the progressive monomer consumptions also supported the monomer-selective living copolymerization. The obtained block copolymer could be functionalized with respect to each segment independently via a repeated Cu(I)-catalyzed azide-alkyne cycloaddition (CuAAC) click chemistry; the alkynyl (propargyl) group was deprotected with tetrabutylammonium fluoride (TBAF) in acetic acid, and the subsequent CuAAC reaction with benzyl azide allowed quantitative and selective modification of the polyacrylate block. Subsequently, the 6-chlorohexyl group was azidated with sodium azide, and the CuAAC reaction with phenylacetylene resulted in complete modification on the polymethacrylate segment. Since CuAAC reaction is selective, quantitative and tolerant to various functional groups, this procedure, that is a combination of monomer-selective copolymerization of reactive monomers with a click chemistry, can provide a facile pathway for the preparation of a block copolymer with a variety of combination of functional pendants groups.