First Observation of the Decay τ⁻to K^(*-)ην_(τ)

Using data recorded by the CLEO-II detector at CESR, we report the first measurement of the branching fraction for the decay of $\tau^-$ into $K^{*-}\eta \nu_{\tau}$. The measured branching fraction is (2.9 +- 0.8 +- 0.4) $10^{-4}$. We also measure the inclusive branching fractions without requiring the $K^*$ resonance: $\tau^-$ into $K_S \pi^- \eta \nu_{\tau}$, $\tau^-$ into $K^- \pi^0 \eta \nu_{\tau}$. The measured branching fractions are (1.10 +- 0.35 +- 0.11) $10^{-4}$, (1.77 +- 0.56 +- 0.71) $10^{-4}$ respectively.