We demonstrate a photonic chip-based all-optical exclusive-OR (XOR) gate for phase-encoded optical signals via four-wave mixing in a highly nonlinear, dispersion-engineered chalcogenide (As2S3) planar waveguide. We achieve error-free, XOR operation for 40 Gbit/s differential phase shift keying (DPSK) optical signals with no power penalty. The effectiveness and broad bandwidth operation of our approach is highlighted by implementing an XOR gate for 160 Gbit/s DPSK signals.