Using three nonlinear dicarboxylates, isophthalate (ipa), 4,4′-oxy-bis(benzoate) (oba), and ethylenedi(4-oxybenzoate) (eoba), we have prepared five neutral infinite copper(II) dicarboxylate coordination polymers containing lateral aromatic chelate ligands, namely [Cu(ipa)(2,2′-bpy)]_n·2nH₂O (1), [Cu₂-(ipa)₂ (phen)₂H₂O]_n (2), [Cu(oba)-(phen)]_n, (3), [Cu(oba)(2,2′-bpy)]_n (4), and [Cu(eoba)(phen)]_n (5; 2,2′-bpy=2,2′-bipyridine, phen = 1,10-phenanthroline) by hydrothermal synthesis. X-ray single-crystal structural analyses of these complexes reveal that the nonlinear flexible or V-shaped dicarboxylates can induce the helicity or flexuousity of the polymeric chains and aromatic chelate ligands are important in providing potential supramolecular recognition sites for π-π aromatic stacking interactions. An appropriate combination of the bridging dicarboxylate and aromatic chelate can induce a pair of single-stranded helical or flexuous chains to generate a double-stranded helix or molecular zipper through supramolecular interactions, respectively.