  $SU(N)$ Yang-Mills theory in three dimensions, with a Chern-Simons term of
level $k$ (an integer) added, has two dimensionful coupling constants, $g^2 k$
and $g^2 N$; its possible phases depend on the size of $k$ relative to $N$. For
$k \gg N$, this theory approaches topological Chern-Simons theory with no
Yang-Mills term, and expectation values of multiple Wilson loops yield Jones
polynomials, as Witten has shown; it can be treated semiclassically. For $k=0$,
the theory is badly infrared singular in perturbation theory, a
non-perturbative mass and subsequent quantum solitons are generated, and Wilson
loops show an area law. We argue that there is a phase transition between these
two behaviors at a critical value of $k$, called $k_c$, with $k_c/N \approx 2
\pm .7$. Three lines of evidence are given: First, a gauge-invariant one-loop
calculation shows that the perturbative theory has tachyonic problems if $k
\leq 29N/12$.The theory becomes sensible only if there is an additional dynamic
source of gauge-boson mass, just as in the $k=0$ case. Second, we study in a
rough approximation the free energy and show that for $k \leq k_c$ there is a
non-trivial vacuum condensate driven by soliton entropy and driving a
gauge-boson dynamical mass $M$, while both the condensate and $M$ vanish for $k
\geq k_c$. Third, we study possible quantum solitons stemming from an effective
action having both a Chern-Simons mass $m$ and a (gauge-invariant) dynamical
mass $M$. We show that if $M \gsim 0.5 m$, there are finite-action quantum
sphalerons, while none survive in the classical limit $M=0$, as shown earlier
by D'Hoker and Vinet. There are also quantum topological vortices smoothly
vanishing as $M \rightarrow 0$.
