We demonstrate chip-based Tbaud optical signal processing for all-optical performance monitoring, switching and demultiplexing based on the instantaneous Kerr nonlinearity in a dispersion-engineered As(2)S(3) planar waveguide. At the Tbaud transmitter, we use a THz bandwidth radio-frequency spectrum analyzer to perform all-optical performance monitoring and to optimize the optical time division multiplexing stages as well as mitigate impairments, for example, dispersion. At the Tbaud receiver, we demonstrate error-free demultiplexing of a 1.28 Tbit/s single wavelength, return-to-zero signal to 10 Gbit/s via four-wave mixing with negligible system penalty (< 0.5 dB). Excellent performance, including high four-wave mixing conversion efficiency and no indication of an error-floor, was achieved. Our results establish the feasibility of Tbaud signal processing using compact nonlinear planar waveguides for Tbit/s Ethernet applications.