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 Bπ mass spectrum in the region 5.6–5.8 GeV is interpreted as resulting from the decay ), where 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 B1* and B2* spin states, as well as the branching fraction for the combination 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.