We obtain the all-loop worldsheet S matrix for fundamental excitations on AdS₃×S³×T⁴ by studying the off-shell symmetry algebra of the superspace action in light cone gauge. The massless modes, unaccounted for in earlier works, are automatically included in our treatment. Their exact dispersion relation is found to be nonrelativistic, of giant-magnon form, and their scattering is naturally well defined. This opens the way to a complete investigation of AdS₃/CFT₂ integrability.