The Chern-Simons theory coupled to complex scalars is quantized on the light-front in the local light-cone gauge by constructing the self-consistent Hamiltonian theory. It is shown that no inconsistency arises on using two local gauge-fixing conditions in the Dirac procedure. The light-front Hamiltonian turns out to be simple and the framework may be useful to construct renormalized field theory of particles with fractional statistics (anyons). The theory is shown to be relativistic and the extra term in the transformation of the matter field under space rotations, interpreted in previous works as anomaly, is argued to be gauge artefact. (author). 20 refs.