  We study adiabatic quantum pumping in the resonant tunneling regime of a
nearly-closed quantum dot, which is coupled to two leads via tunneling
barriers. Using small cyclic variations of the tunneling rates of the barriers
as the pumping mechanism, a current is obtained which depends sensitively on
the system parameters and exhibits peaks due to Coulomb blockade. The
distribution of the peak heights is found for temperatures $\Gam \ll k_{B} T
\ll \Delta$, with $\Gam$ the total decay width into the leads and $\Delta$ the
single-particle level spacing of the dot, and their average height is predicted
to increase by a factor of $\frac{5\sqrt{2}}{18} \pi \approx 1.2$ upon breaking
time-reversal symmetry. This is the pumping analog of the statistical theory of
Coulomb blockade conductance peaks.
