  The $\eta \pi^{-}$ system has been studied in the reaction $\pi^{-} p \to
\eta \pi^{-} p$ at 18 GeV/c. A large asymmetry in the angular distribution is
observed indicating interference between L-even and L-odd partial waves. The
$a_{2}(1320)$ is observed in the $J^{PC}$ = $2^{++}$ wave, as is a broad
enhancement between 1.2 and 1.6 GeV/c^{2} in the $J^{PC} = 1^{-+}$ wave. The
observed phase difference between these waves shows that there is phase motion
in addition to that due to $a_{2}(1320)$ decay. The data can be fitted by
interference between the $a_{2}(1320)$ and an exotic $1^{-+}$ resonance with $M
= (1370 \pm 16 {+50}\atop{-30}$) MeV/c^2 and $\Gamma =(385 \pm 40
{+65}\atop{-105}$) MeV/c^2.
