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We propose, design, and experimentally demonstrate a nonlocal metasurface with frequency-selective, wavefront shaping capabilities and at the same time polarization-selective chiral response. This operation requires the implementation of bilayer metasurfaces with engineered nonlocal response, wherein each layer controls locally a specific linear polarization, while the coupled system supports arbitrary polarization states. We demonstrate that this platform enables unprecedented control over wavefront manipulation, including frequency-selective, spin-selective reflection with arbitrary geometric phase. We observe a highly chiral response with record-high reflectance efficiency over a narrow frequency window, both for a uniform metasurface and for one with tailored phase gradient for anomalous reflection. Both devices provide an efficiency well above the theoretical limit of 25% for conventional single-layer devices. Our work opens exciting opportunities for augmented reality and enhanced secure wireless communications.