Matter structured on a length scale comparable to or smaller than the wavelength of light can exhibit unusual optical properties(1). Particularly promising components for such materials are metal nanostructures, where structural alterations provide a straightforward means of tailoring their surface plasmon resonances and hence their interaction with light(2,3). But the top-down fabrication of plasmonic materials with controlled optical responses in the visible spectral range remains challenging, because lithographic methods are limited in resolution and in their ability to generate genuinely three-dimensional architectures(4,5). Molecular self-assembly(6,7) provides an alternative bottom-up fabrication route not restricted by these limitations, and DNA-and peptide-directed assembly have proved to be viable methods for the controlled arrangement of metal nanoparticles in complex and also chiral geometries(8-14). Here we show that DNA origami(15,16) enables the high-yield production of plasmonic structures that contain nanoparticles arranged in nanometre-scale helices. We find, in agreement with theoretical predictions(17), that the structures in solution exhibit defined circular dichroism and optical rotatory dispersion effects at visible wavelengths that originate from the collective plasmon-plasmon interactions of the nanoparticles positioned with an accuracy better than two nanometres. Circular dichroism effects in the visible part of the spectrum have been achieved by exploiting the chiral morphology of organic molecules and the plasmonic properties of nanoparticles(18-20), or even without precise control over the spatial configuration of the nanoparticles(12,21,22). In contrast, the optical response of our nanoparticle assemblies is rationally designed and tunable in handedness, colour and intensity-in accordance with our theoretical model.