  We analyze the partial rate asymmetry in $B^{\pm} \to P {\bar P} \pi^{\pm}$
decays ($ P = \pi^+, K ^+, \pi^0, \eta$) which results from the interference of
the nonresonant decay amplitude and the resonant amplitude for $B^{\pm} \to
\chi_{c0} \pi^{\pm} $ followed by the decay $\chi_{c0} \to P {\bar P} $. The CP
violating phase $\gamma$ can be extracted from the measured asymmetry. We find
that the partial rate asymmetry for $B^\pm \to \pi^+ \pi^- \pi^\pm$ is
$0.33~sin \gamma$, while for $B^\pm \to K^+ K^-\pi^\pm$ it amounts $0.45~ sin
\gamma$.
