We present a preliminary measurement of the branching fraction of the $B$ meson decay \\ $B^0 \rightarrow a_1^+(1260) \pi^-$ with $a_1^+(1260) \rightarrow \pi^+ \pi^+ \pi^-$. The data were recorded with the BaBaR detector at the SLAC $B$ factory PEP-II and correspond to $124\times 10^6$ $B \bar{B}$ pairs produced in $e^+ e^-$ annihilation through the $\Ypsilon(4S)$ resonance. We find the branching fraction ${\cal B}(B^0 \rightarrow a_1^+(1260) \pi^-) = (42.6 \pm 4.2 \pm 4.1) \times 10^{-6}$. The fitted values of the $a_1(1260)$ parameters are $m_{a_1}=1.19 \pm 0.02$ $GeV/c^2$ and $\Gamma_{a_1} = 312 \pm 55$ $MeV/c^2$.