The protein-only infectious agents known as prions exist within cellular matrices as populations of assembled polypeptide phases ranging from particles to amyloid fibres. These phases appear to undergo Darwinian-like selection and propagation, yet remarkably little is known about their accessible chemical and biological functions. Here we construct simple peptides that assemble into well-defined amyloid phases and define paracrystalline surfaces able to catalyse specific enantioselective chemical reactions. Structural adjustments of individual amino acid residues predictably control both the assembled crystalline order and their accessible catalytic repertoire. Notably, the density and proximity of the extended arrays of enantioselective catalytic sites achieve template-directed polymerization of new polymers. These diverse amyloid templates can now be extended as dynamic self-propagating templates for the construction of even more complex functional materials.