  A model for the $B^\pm \to \pi^-\pi^+\pi^\pm$ decay amplitude is proposed to
study the large CP violation observed at the high mass region of the Dalitz
plane. A short distance $ b \to u $ amplitude with the weak phase $\gamma$ is
considered together with the contribution of a hadronic charm loop and a s-wave
$D\bar{D}\to \pi\pi$ rescattering. In the model, the $\chi_c^0$ appears as a
narrow resonant state of the $D\bar D$ system below threshold. It is introduced
in an unitary two channel S-matrix model of the coupled $D\bar D$ and $\pi\pi$
channels, where the $\chi_c^0$ complex pole in $D\bar D$ channel shows its
signature in the off-diagonal matrix element and in the associated $D\bar{D}\to
\pi\pi$ transition amplitude. The strong phase of the resulting decay amplitude
has a sharp sign change at the $D\bar D$ threshold, changing the sign of the CP
asymmetry, as it is observed in the data. We conclude that the hadronic charm
loop and rescattering mechanism are relevant to the broadening of the CP
asymmetry around the $\chi_c^0$ resonance in the $\pi\pi$ channel. This novel
mechanism provides a possible interpretation of the CP asymmetry defier
experimental result presented by the LHCb collaboration for the $B^\pm \to
\pi^-\pi^+\pi^\pm$ decay in the high mass region.
