The double helix of DNA epitomizes this molecule's ability to self-assemble in aqueous solutions into a complex chiral structure using hydrogen bonding and hydrophobic interactions. Non-covalently interacting molecules in organic solvents are used to design systems that similarly form controlled architectures1, 2, 3, 4, 5, 6, 7. Peripheral chiral centres in assemblies8, 9 and chiral side chains attached to a polymer backbone10, 11 have been shown to induce chirality at the supramolecular level, and highly ordered structures stable in water are also known12, 13, 14, 15. However, it remains difficult to rationally exploit non-covalent interactions for the formation of chiral assemblies that are stable in water, where solvent molecules can compete effectively for hydrogen bonds. Here we describe a general strategy for the design of functionalized monomer units and their association in either water or alkanes into non-covalently linked polymeric structures with controlled helicity and chain length. The monomers consist of bifunctionalized ureidotriazine units connected by a spacer and carrying solubilizing chains at the periphery. This design allows for dimerization through self-complementary quadruple hydrogen bonding between the units and solvophobically induced stacking of the dimers into columnar polymeric architectures, whose structure and helicity can be adjusted by tuning the nature of the solubilizing side chains.