  We have observed new channels for $\tau$ decays with an $\eta$ in the final
state. We study 3-prong tau decays, using the $\eta\to\gamma\gamma$ and
$\eta\to 3\piz$ decay modes and 1-prong decays with two $\piz$'s using the
$\eta\to\gamma\gamma$ channel. The measured branching fractions are
$\B(\tau^{-}\to \pi^{-}\pi^{-}\pi^{+}\eta\nu_{\tau})
  =(3.4^{+0.6}_{-0.5}\pm0.6)\times10^{-4}$ and $\B(\tau^{-}\to
\pi^{-}2\piz\eta\nu_{\tau}
  =(1.4\pm0.6\pm0.3)\times10^{-4}$. We observe clear evidence for
$f_1\to\eta\pi\pi$ substructure and measure $\B(\tau^{-}\to
f_1\pi^{-}\nu_{\tau})=(5.8^{+1.4}_{-1.3}\pm1.8)\times10^{-4}$. We have also
searched for $\eta'(958)$ production and obtain 90% CL upper limits
$\B(\tau^{-}\to \pi^{-}\eta'\nu_\tau)<7.4\times10^{-5}$ and $\B(\tau^{-}\to
\pi^{-}\piz\eta'\nu_\tau)<8.0\times10^{-5}$.
