  The Next to Minimal Supersymmetric Standard Model (NMSSM), proposed as a
solution of the mu problem of the Minimal Supersymmetric Standard Model, has a
discrete Z_{3} symmetry which is spontaneously broken at the electroweak phase
transition, resulting in a cosmological domain wall problem. In most cases this
domain wall problem cannot be solved by explicit Z_{3} breaking without
introducing supergravity tadpole corrections which destabilize the weak scale
hierarchy. Here we consider the possibility of solving the domain wall problem
of the NMSSM via spontaneous discrete symmetry breaking occuring during
inflation. For the case where the discrete symmetry breaking field has
renormalizible couplings to the NMSSM fields, we find that the couplings must
be less than 10^{-5} if the reheating temperature is larger than 10^{7}GeV, but
can be up to 10^{-3} for reheating temperatures of the order of the electroweak
phase transition temperature. For the case of non-renormalizible couplings, we
present a model which can solve the domain wall problem for large reheating
temperatures without requiring any very small coupling constants.
  In this model the domain walls are eliminated by a pressure coming from their
interaction with a coherently oscillating scalar field whose phase is fixed
during inflation.
  This oscillating scalar field typically decays after the electroweak phase
transition but before nucleosynthesis, leaving no additional
  Z_{3} symmetry breaking in the zero-temperature theory.
