  We present a model of inflation in a supergravity framework in the Einstein
frame where the Higgs field of the next to minimal supersymmetric standard
model (NMSSM) plays the role of the inflaton. Previous attempts which assumed
non-minimal coupling to gravity failed due to a tachyonic instability of the
singlet field during inflation. A canonical K\"{a}hler potential with
\textit{minimal coupling} to gravity can resolve the tachyonic instability but
runs into the $\eta$-problem. We suggest a model which is free of the
$\eta$-problem due to an additional coupling in the K\"{a}hler potential which
is allowed by the Standard Model gauge group. This induces directions in the
potential which we call K-flat. For a certain value of the new coupling in the
(N)MSSM, the K\"{a}hler potential is special, because it can be associated with
a certain shift symmetry for the Higgs doublets, a generalization of the shift
symmetry for singlets in earlier models. We find that K-flat direction has
$H_u^0=-H_d^{0*}.$ This shift symmetry is broken by interactions coming from
the superpotential and gauge fields. This direction fails to produce successful
inflation in the MSSM but produces a viable model in the NMSSM. The model is
specifically interesting in the Peccei-Quinn (PQ) limit of the NMSSM. In this
limit the model can be confirmed or ruled-out not just by cosmic microwave
background observations but also by axion searches.
