We develop a method to compute the sphaleron rate in the electroweak b
roken phase nonperturbatively. The rate is somewhat slower than a pert
urbative 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 er
asure after the phase transition is prevented only when (lambda/g(2))l
ess than or equal to 0.036. (C) 1998 Elsevier Science B.V. All rights
reserved.