  It has been observed that a large lepton asymmetry, n_{L}/s \approx 0.1, can
prevent the Higgs expectation value from going to zero at high temperature,
resulting in the non-restoration of the SU(2)XU(1) gauge symmetry and other
symmetries. This could allow for the elimination of domain walls and other
dangerous topological defects. Here we show that if the reheating temperature
after inflation, T_{R}, is sufficiently low then symmetry non-restoration will
occur with an asymmetry of the order of the observed baryon asymmetry, n_{B}/s
\approx 10^{-10}. For this to occur T_{R} \leq 1 GeV is necessary. Remarkably,
this happens to be the reheating temperature expected in Affleck-Dine
baryogenesis along a d=6 flat direction of the MSSM. As an example, we show
that this can neatly solve the Z_{3} domain wall problem of the NMSSM.
