  Properties of the Kondo effect in quantum dots depend sensitively on the
coupling parameters and so on the realization of the quantum dot -- the Kondo
temperature itself becomes a mesoscopic quantity. Assuming chaotic dynamics in
the dot, we use random matrix theory to calculate the distribution of both the
Kondo temperature and the conductance in the Coulomb blockade regime. We study
two experimentally relevant cases: leads with single channels and leads with
many channels. In the single-channel case, the distribution of the conductance
is very wide as $T_K$ fluctuates on a logarithmic scale. As the number of
channels increases, there is a slow crossover to a self-averaging regime.
