The combination of multiple orthogonal interactions enables hierarchical complexity in self‐assembled nanoscale materials. Here, efficient supramolecular polymerization of DNA origami nanostructures is demonstrated using a multivalent display of small molecule host–guest interactions. Modification of DNA strands with cucurbit[7]uril (CB[7]) and its adamantane guest, yielding a supramolecular complex with an affinity of order 1010 m−1, directs hierarchical assembly of origami monomers into 1D nanofibers. This affinity regime enables efficient polymerization; a lower‐affinity β‐cyclodextrin–adamantane complex does not promote extended structures at a similar valency. Finally, the utility of the high‐affinity CB[7]–adamantane interactions is exploited to enable responsive enzymatic actuation of origami nanofibers assembled using peptide linkers. This work demonstrates the power of high‐affinity CB[7]–guest recognition as an orthogonal axis to drive self‐assembly in DNA nanotechnology.