Mode structure in a circular chirowaveguide with dielectric lined walls is investigated. By adjusting the dielectric lining thickness and permittivity for a given chiral medium, it is possible to have the eigenmodes categorized as almost right circularly polarized or almost left circularly polarized over a wide frequency band. Such chirowaveguides with modes having high circular polarization purity can serve as feeds of reflector antennas using polarization diversity.