  We develop a method to compute the sphaleron rate in the electroweak broken
phase nonperturbatively. The rate is somewhat slower than a perturbative
estimate. In SU(2) X U(1) Higgs theory at the physical value of Theta_W, and
assuming that the latent heat of the phase transition reheats the universe to
the equilibrium temperature, baryon number erasure after the phase transition
is prevented only when lambda/g^2 <= 0.036.
