  We measure the masses, decay widths and relative production rate of orbitally
excited B mesons using 1.25 million hadronic Z decays recorded by the L3
detector. B-meson candidates are inclusively reconstructed and combined with
charged pions produced at the primary event vertex. An excess of events above
the expected background in the B\pi mass spectrum in the region 5.6-5.8 GeV is
interpreted as resulting from the decay B_u,d^** -> B^(*)\pi, where B_u,d^**
denotes a mixture of l=1 B-meson states containing a u or a d quark. A fit to
the mass spectrum yields the masses and decay widths of the B_1^* and B_2^*
spin states, as well as the branching fraction for the combination of l=1
states. In addition, evidence is presented for the existence of an excited
B-meson state or mixture of states in the region 5.9-6.0 GeV.
