We present a measurement of the branching fraction for the decay of the neutral B meson into the final state J/ψπ+π-. The data set contains approximately 56×106 BB̅ pairs produced at the Υ(4S) resonance and recorded with the BABAR detector at the PEP-II asymmetric-energy e+e- storage ring. The result of this analysis is B(B0→J/ψπ+π-)=(4.6±0.7±0.6)×10-5, where the first error is statistical and the second is systematic. In addition, we measure B(B0→J/ψρ0)=(1.6±0.6±0.4)×10-5.
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