We report the results of a CP violation analysis of the decay B±→Dπ+π-π0K±, where Dπ+π-π0 indicates a neutral D meson detected in the final state π+π-π0, excluding KS0π0. The analysis makes use of 324×106 e+e-→BB̄ events recorded by the BABAR experiment at the PEP-II e+e- storage ring. Analyzing the π+π-π0 Dalitz plot distribution and the B±→Dπ+π- π0K± branching fraction and decay rate asymmetry, we find the following one-standard-deviation constraints on the amplitude ratio and on the weak and strong phases: 0.06<rB<0.78, -30°<γ<76°, -27°<δ<78°. We also measure the magnitudes and phases of the components of the D0→π+π-π0 decay amplitude. © 2007 The American Physical Society.