  We calculate production rates for massless $(u,d)$ and massive $(s,c,b)$
quarks in pure glue and quark gluon plasmas to leading order in the strong
coupling constant $g$. The leading contribution comes from gluon decay into
$q\bar q$ pairs, using a thermal gluon propagator with finite thermal mass and
damping rate. The rate behaves as $\alpha_S^2(\ln 1/\alpha_S)^2 T^4$ when $m,
\alpha_S \rightarrow 0$ and depends linearly on the transverse gluon damping
rate for all values of the quark mass $m$. The light quark ($u$, $d$, $s$)
chemical equilibration time is approximately 10-100 $T^{-1}$ for $g=$2-3, so
that quarks are likely to remain far from chemical equilibrium in
ultrarelativistic nuclear collisions.
