  The exclusive reaction $\pi^- p \to \eta \pi^0 n$, $\eta \to \pi^+ \pi^-
\pi^0$ at 18 GeV$/c$ has been studied with a partial wave analysis on a sample
of 23~492 $\eta \pi^0 n$ events from BNL experiment E852. A mass-dependent fit
is consistent with a resonant hypothesis for the $P_+$ wave, thus providing
evidence for a neutral exotic meson with $J^{PC} = 1^{-+}$, a mass of $1257 \pm
20 \pm 25$ MeV$/c^2$, and a width of $354 \pm 64 \pm 60$ MeV$/c^2$. New
interpretations of the meson exotics in neutral $\eta \pi^0$ system observed in
E852 and Crystal Barrel experiments are discussed.
