  In an abelian topologically massive gauge theory, any eigenstate of the
Hamiltonian can be decomposed into a factor describing massive propagating
gauge bosons and a Chern-Simons wave function describing a set of
nonpropagating ``topological'' excitations. The energy depends only on the
propagating modes, and energy eigenstates thus occur with a degeneracy that can
be parametrized by the Hilbert space of the pure Chern-Simons theory. We show
that for a {\em nonabelian} topologically massive gauge theory, this degeneracy
is lifted: although the Gauss law constraint can be solved with a similar
factorization, the Hamiltonian couples the propagating and nonpropagating
(topological) modes.
