  We propose a model of inflation based on a simple variant of the NMSSM,
called $\phi$NMSSM, where the additional singlet $\phi$ plays the role of the
inflaton in hybrid (or inverted hybrid) type models. As in the original NMSSM,
the $\phi$NMSSM solves the $\mu$ problem of the MSSM via the VEV of a gauge
singlet $N$, but unlike the NMSSM does not suffer from domain wall problems
since the offending $Z_3$ symmetry is replaced by an approximate Peccei-Quinn
symmetry which also solves the strong CP problem, and leads to an invisible
axion with interesting cosmological consequences. The PQ symmetry may arise
from a superstring model with an exact discrete $Z_3 \times Z_5$ symmetry after
compactification. The model predicts a spectral index $n=1$ to one part in
$10^{12}$.
