  We discuss the canonical quantization of Chern-Simons theory in $2+1$
dimensions, minimally coupled to a Dirac spinor field, first in the temporal
gauge and then in the Coulomb gauge. In our temporal gauge formulation, Gauss's
law and the gauge condition, $A_0 = 0$, are implemented by embedding the
formulation in an appropriate physical subspace. We construct a Fock space of
charged particle states that satisfy Gauss's law, and show that they obey
fermion, not fractional statistics. The gauge-invariant spinor field that
creates these charged states from the vacuum obeys the anticommutation rules
that generally apply to spinor fields. The Hamiltonian, when described in the
representation in which the charged fermions are the propagating particle
excitations that obey Gauss's law, contains an interaction between charge and
transverse current densities. We observe that the implementation of Gauss's law
and the gauge condition does not require us to use fields with graded
commutator algebras or particle excitations with fractional statistics. In our
Coulomb gauge formulation, we implement Gauss's law and the gauge condition,
$\partial_lA_l=0$, by the Dirac-Bergmann procedure. In this formulation, the
constrained gauge fields become functionals of the spinor fields, and are not
independent degrees of freedom. The formulation in the Coulomb gauge confirms
the results we obtained in the temporal gauge: The ``Dirac-Bergmann''
anticommutation rule for the charged spinor fields $\psi$ and $\psi^\dagger$
that have both been constrained to obey Gauss's law, is precisely identical to
the canonical spinor anticommutation rule that generates standard fermion
statistics. And we also show that the Hamiltonians for charged particle states
in our temporal and Coulomb gauge formulations are identical, once Gauss's law
