The BES data on the $J/\psi \to \eta K^{\star 0} \bar{K}^{\star0}$ reaction show a clear enhancement in the $K^{\star 0} \bar{K}^{\star 0}$ mass distribution close to the threshold of this channel. Such an enhancement is usually a signature of a L=0 resonance around threshold, which in this case would correspond to an $h_1$ state with quantum numbers $I^G(J^{PC})=0^-(1^{+-})$. A state around 1800 MeV results from the interaction of the $K^{\star} \bar{K}^{\star}$ using the local hidden gauge approach. We show that the peak observed in $J/\psi \to \eta K^{\star 0} \bar{K}^{\star 0}$ naturally comes from the creation of this $h_1$ state with mass and width around 1830 MeV and 110 MeV, respectively. A second analysis, model independent, corroborates the first result, confirming the relationship of the enhancement in the invariant mass spectrum with the $h_1$ resonance.