  We investigate the $\eta \bar{K}K^*$ three body system in order to look for
possible $I^G(J^{PC})=0^+(1^{-+})$ exotic states in the framework of the fixed
center approximation to the Faddeev equation. We assume the scattering of
$\eta$ on a clusterized system $\bar{K}K^*$, which is known to generate the
$f_1(1285)$, or a $\bar{K}$ on a clusterized system $\eta K^*$, which is shown
to generate the $K_1(1270)$. In the case of the
$\eta$-$(\bar{K}K^*)_{f_1(1285)}$ scattering, we find evidence of a bound state
$I^G(J^{PC})=0^+(1^{-+})$ below the $\eta{f_1(1285)}$ threshold with mass
around 1700 MeV and width about 180 MeV. Considering the $\bar{K}$-$(\eta
K^*)_{K_1(1270)}$ scattering, we obtain a bound state $I(J^{P})=0(1^{-})$ just
below the $\bar{K}{K_1(1270)}$ threshold with a mass around 1680 MeV and a
width about 160 MeV.
