  We present measurements of CP-violating asymmetries in the decay B0 ->
a_1(1260)^{+-} pi^{-+} with a_1(1260)^{+-} -> pi^{-+} pi^{+-} pi^{+-}. The data
sample corresponds to 384 million B B-bar pairs collected with the BaBar
detector at the PEP-II asymmetric B-factory at SLAC. We measure the
CP-violating asymmetry A^{a_1 \pi}_{CP}=-0.07+-0.07+-0.02, the mixing-induced
CP violation parameter S_{a_1 \pi}= 0.37 +-0.21+-0.07, the direct CP violation
parameter C_{a_1 \pi}=-0.10+-0.15+-0.09, and the parameters \Delta C_{a_1
\pi}=0.26+-0.15+-0.07 and \Delta S_{a_1\pi}=-0.14+-0.21+-0.06. From these
measured quantities we determine the angle \alpha_{\rm eff}= 78.6^{\circ} +-
7.3^{\circ}.
