First Observation of the Decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mi/><mml:mo>→</mml:mo><mml:mi/><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">K</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="italic">η</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>τ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>

The decay ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{*\ensuremath{-}}\ensuremath{\eta}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ has been observed with the CLEO II detector. The ${K}^{*\ensuremath{-}}$ is reconstructed in two decay channels, ${K}^{*\ensuremath{-}}\ensuremath{\rightarrow}{K}_{S}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${K}^{*\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$. The $\ensuremath{\eta}$ is reconstructed from the decay $\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$. The measured branching fraction is $B({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{*\ensuremath{-}}\ensuremath{\eta}{\ensuremath{\nu}}_{\ensuremath{\tau}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(2.9\ifmmode\pm\else\textpm\fi{}0.8\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. We also measure the inclusive branching fractions without requiring the ${K}^{*}$ resonance, $B({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}_{S}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta}{\ensuremath{\nu}}_{\ensuremath{\tau}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(1.10\ifmmode\pm\else\textpm\fi{}0.35\ifmmode\pm\else\textpm\fi{}0.11)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and $B({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}\ensuremath{\eta}{\ensuremath{\nu}}_{\ensuremath{\tau}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(1.77\ifmmode\pm\else\textpm\fi{}0.56\ifmmode\pm\else\textpm\fi{}0.71)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. The results indicate that the ${K}^{*\ensuremath{-}}$ resonance dominates the ${K}_{S}{\ensuremath{\pi}}^{\ensuremath{-}}$ mass spectrum.