  The mean field like gauge invariant variational method formulated recently,
is applied to a topologically massive QED in 3 dimensions. We find that the
theory has a phase transition in the Chern Simons coefficient $n$. The phase
transition is of the Berezinsky-Kosterlitz - Thouless type, and is triggered by
the liberation of Polyakov monopoles, which for $n>8$ are tightly bound into
pairs. In our Hamiltonian approach this is seen as a similar behaviour of the
magnetic vortices, which are present in the ground state wave functional of the
compact theory. For $n>8$, the low energy behavior of the theory is the same as
in the noncompact case. For $n<8$ there are no propagating degrees of freedom
on distance scales larger than the ultraviolet cutoff. The distinguishing
property of the $n<8$ phase, is that the magnetic flux symmetry is
spontaneoously broken.
