A general strategy for creating nanocavities with tunable sizes based on the folding of unnatural oligomers is presented. The backbones of these oligomers are rigidified by localized, three-center intramolecular hydrogen bonds, which lead to well-defined hollow helical conformations. Changing the curvature of the oligomer backbone leads to the adjustment of the interior cavity size. Helices with interior cavities of 10 Å to >30 Å across, the largest thus far formed by the folding of unnatural foldamers, are generated. Cavities of these sizes are usually seen at the tertiary and quaternary structural levels of proteins. The ability to tune molecular dimensions without altering the underlying topology is seen in few natural and unnatural foldamer systems.