We analyze the asymmetry in the partial widths for the decays B ±→M M ̄ π ± ( M= π +, K +, π 0, η), which results from the interference of the nonresonant decay amplitude with the resonant amplitude for B ±→ χ c0 π ± followed by the decay χ c0→M M ̄ . The CP violating phase γ can be extracted from the measured asymmetry. We find that the partial width asymmetry for B ±→ π + π − π ± is about 0.33 sinγ , and about 0.45 sinγ for B ±→ K + K − π ±, while it is somewhat smaller for B ±→ π 0 π 0 π ± and B ±→ ηηπ ±. Potential sources of uncertainties in these results, primarily coming from poorly known input parameters, are discussed.