We report the results of a study of the exclusive charmless semileptonic decay, B 0 → π − ℓ + ν , undertaken with approximately 227 × 10 6 B ¯¯¯ B pairs collected at the Υ ( 4 S ) resonance with the BABAR detector. The analysis uses events in which the signal B decays are reconstructed with an innovative loose neutrino reconstruction technique. We obtain partial branching fractions in 12 bins of q 2 , the momentum transfer squared, from which we extract the f + ( q 2 ) form-factor shape and the total branching fraction B ( B 0 → π − ℓ + ν ) = ( 1.46 ± 0.07 stat ± 0.08 syst ) × 10 − 4 . Based on a recent unquenched lattice QCD calculation of the form factor in the range q 2 > 16     GeV 2 , we find the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element | V u b | to be ( 4.1 ± 0.2 stat ± 0.2 syst + 0.6 − 0.4 FF ) × 10 − 3 , where the last uncertainty is due to the normalization of the form factor.