  We report a measurement of the branching fractions of Bbar -> D** l^- nubar_l
decays based on 417 fb-1 of data collected at the Upsilon(4S) resonance with
the BaBar detector at the PEP-II e+e- storage rings. Events are selected by
fully reconstructing one of the B mesons in a hadronic decay mode. A fit to the
invariant mass differences m(D(*)pi)-m(D(*)) is performed to extract the signal
yields of the different D** states. We observe the Bbar -> D** l^- nubar_l
decay modes corresponding to the four D** states predicted by Heavy Quark
Symmetry with a significance greater than six standard deviations including
systematic uncertainties.
