  Shell Model Monte Carlo (SMMC) techniques are used to calculate two-neutrino
double beta decay matrix elements. We validate the approach against direct
diagonalization for $^{48}$Ca in the complete $pf$-shell using the KB3
interaction. The method is then applied to the decay of $^{76}$Ge in the
$(0f_{5/2},1p,0g_{9/2})$ model space using a newly calculated realistic
interaction. Our result for the matrix element is $0.13\pm0.05$ MeV$^{-1}$, in
agreement with the experimental value.
