  We investigate baryogenesis at a first order electroweak phase transition in
the presence of a CP violating condensate on the bubble walls, in the regime in
which the bubble walls are `thick', in the sense that fermions interact with
the plasma many times as the bubble wall passes. Such a condensate is present
in multi-Higgs extensions of the standard model and may be formed via an
instability in the minimal standard model. We concentrate on particles with
typical thermal energies in the plasma, whose interactions with the wall are
accurately described by the WKB approximation, in which a classical chiral
force is evident. The deviations from thermal equilibrium produced by motion of
the wall are then treated using a classical Boltzmann equation which we solve
in a fluid approximation. From the resulting equations we find two effects
important for baryogenesis: (i) a classical chiral force term due to the $CP$
violating background, and (ii) a term arising from hypercharge violating
interactions which are pushed out of equilibrium by the background{field.
Provided the wall propagates slower than the speed of sound, both terms lead to
the diffusion of a chiral asymmetry in front of the wall. This can produce a
baryon asymmetry of the observed magnitude for typical wall velocities and
thicknesses.
