  The equation of state of beta-stable and charge neutral nucleonic matter is
computed within the SU(2) parity doublet model in mean field and in the
relativistic Hartree approximation. The mass of the chiral partner of the
nucleon is assumed to be 1200 MeV. The transition to the chiral restored phase
turns out to be a smooth crossover in all the cases considered, taking place at
a baryon density of just $2\rho_0$. The mass-radius relations of compact stars
are calculated to constrain the model parameters from the maximum mass limit of
neutron stars. It is demonstrated that chiral symmetry starts to be restored,
which in this model implies the appearance of the chiral partners of the
nucleons, in the center of neutron stars. However, the analysis of the decay
width of the assumed chiral partner of the nucleon poses limits on the validity
of the present version of the model to describe vacuum properties.
