  We present the results of a lattice computation of the form factors for B^0
->pi^- l^+nu_l decays near zero-recoil. These results will allow a
determination of the CKM matrix element |Vub| when measurements of the
differential decay rate become available. We also provide models for
extrapolation of the form factors and rate to the full recoil range. Our
computation is performed in the quenched approximation to QCD on a 24^3x48
lattice at beta=6.2, using a non-perturbatively O(a)-improved action. The
masses of all light valence quarks involved are extrapolated to their physical
values.
