We report a measurement of CP-violating asymmetries in B0→(ρπ) 0→π+π-π0 decays using a time-dependent Dalitz plot analysis. The results are obtained from a data sample of 375×106 Υ(4S) →BB̄ decays, collected by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We measure 26 coefficients of the bilinear form-factor terms occurring in the time-dependent decay rate of the B0 meson. We derive the physically relevant quantities from these coefficients. In particular, we measure a constraint on the angle α of the unitarity triangle. © 2007 The American Physical Society.