  The self-energy of an eta meson in the nuclear medium is calculated in a
chiral unitary approach.
  A coupled channel Bethe-Salpeter equation is solved to obtain the effective
eta-N interaction in the medium.
  The base model reproduces well the free space pi-N elastic and inelastic
scattering at the eta-N threshold or N^*(1535) region.
  The Pauli blocking on the nucleons, binding potentials for the baryons and
self-energies of the mesons are incorporated, including the eta self-energy in
a self-consistent way.
  Our calculation predicts about -54 -i29 MeV for the optical potential at
normal nuclear matter for an eta at threshold but also shows a strong energy
dependence of the potential.
