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We measure the relative rate of production of orbitally excited (L=1) states of B mesons (B**) by observing their decays into B π ±. We reconstruct B mesons through semileptonic decay channels using data collected in pp̅ collisions at √s =1.8 TeV. The fraction of light B mesons that are produced as L=1B** states is measured to be 0.28±0.06(stat) ±0.03(syst). We also measure the collective mass of the B** states, and quantify the result by quoting the (model-dependent) mass of the lowest B** state to be m (B1)=5.71 ±0.02 GeV/c2.