We propose a novel dual-band chiral metasurface that offers arbitrary polarization control of electromagnetic waves. By cascading an array of multiple concentric rectangular rings and precisely rotating each array, we physically encode certain surface impedances at two different frequency bands and realize a dual-band tensor impedance metasurface. Such a meta-surface can be configured to perform general chiral operations. We demonstrate the versatility of the proposed structure through a design example of a dual-band circular polarization selective surface.