  One of the most efficient mechanisms for producing the baryon asymmetry of
the Universe is the decay of scalar condensates in a SUSY GUT as was first
suggested by Affleck and Dine. We show that given a large enough asymmetry, the
baryon number will be preserved down to low temperatures even if B - L = 0,
because the baryon number carrying scalars form bose condensates that give the
W a mass. We derive the conditions on the condensate needed to suppress
electroweak sphaleron interactions which would otherwise drive the baryon
asymmetry to zero when B - L = 0.
