A novel and advanced photovoltaic concentrator optic is presented comprising a Fresnel lens and a dielectric solid RXI as a secondary optical element, both with free-form surfaces (i.e. neither rotational nor linear symmetry). The RXI secondary is designed with the Simultaneous Multiple Surface (SMS) design method of Nonimaging Optics. In the secondary optics rays undergo refraction (R), reflection (X) and total internal reflection (I), so SMS nomenclature [2] for the device is RXI assigning letters to each surface that deflects rays. This is the first time the RXI-type geometry has been applied to design a photovoltaic secondary element. The LPI patented Fresnel- RXI Köhler concentrator [1] produces both the desired light concentration with high tolerance (high acceptance angle) as well as high irradiance uniformity on the solar cell achieved by Köhler integration method. The optical performance of the FRXI device (F denotes a Fresnel lens surface) will be presented as well as comparison with other conventional Fresnel-based CPV concentrators and application of the designed system.