  We canonically quantize $(2+1)$-dimensional electrodynamics including a
higher-derivative Chern-Simons term. The effective theory describes a standard
photon and an additional degree of freedom associated with a massive ghost. We
find the Hamiltonian and the algebra satisfied by the field operators. The
theory is characterized by an indefinite metric in the Hilbert space that
brings up questions on causality and unitarity. We study both of the latter
fundamental properties and show that microcausality as well as perturbative
unitarity up to one-loop order are conserved when the Lee-Wick prescription is
employed.
