We report the first demonstration of on-chip cascaded stimulated Brillouin scattering (SBS). Cascaded SBS is characterized in a 4 cm long chalcogenide (As₂S₃) rib waveguide where the end facet reflections provide a monolithic Fabry-Perot (FP) resonator. The presence of the FP cavity reduces the Brillouin gain threshold, which enables observation of cascaded SBS at reduced pump powers. We observe up to three orders of Stokes waves in the backscattered signal at a coupled peak power of 1.34 W. Anti-Stokes waves due to four-wave mixing between the pump and the Stokes wave were observed in the forward spectrum.