  We study dynamical symmetry breaking in three-dimensional QED with a
Chern-Simons (CS) term, considering the screening effect of $N$ flavor
fermions. We find a new phase of the vacuum, in which both the fermion mass and
a magnetic field are dynamically generated, when the coefficient of the CS term
$\kappa$ equals $N e^2/4 \pi$. The resultant vacuum becomes the finite-density
state half-filled by fermions. For $\kappa=N e^2/2 \pi$, we find the fermion
remains massless and only the magnetic field is induced. For $\kappa=0$,
spontaneous magnetization does not occur and should be regarded as an external
field.
