We introduce core-shell plasmonic nanohelices, highly tunable structures that have a different response in the visible for circularly polarized light of opposite handedness. The glass core of the helices is fabricated using electron beam induced deposition and the pure gold shell is subsequently sputter coated. Optical measurements allow us to explore the chiral nature of the nanohelices, where differences in the response to circularly polarized light of opposite handedness result in a dissymmetry factor of 0.86, more than twice of what has been previously reported. Both experiments and subsequent numerical simulations demonstrate the extreme tunability of the core-shell structures, where nanometer changes to the geometry can lead to drastic changes of the optical responses. This tunability, combined with the large differential transmission, make core-shell plasmonic nanohelices a powerful nanophotonic tool for, for example, (bio)sensing applications.