The copper-catalyzed cross-coupling of alkynes and α-diazoesters has been applied in the synthesis of polyallenoates for the first time. The polymerization tolerated various functional groups and afforded the polyallenoates with high molecular weight. With chiral guanidinium bromide as a ligand, the axial chirality of the allene moiety could be generated with high enantioselectivity during the polymerization process.