We measure the relative rate of production of orbitally excited (L=1) states of B mesons (B**) by observing their decays into B\u3c0\ub1. We reconstruct B mesons through semileptonic decay channels using data collected pp\u304 collisions at 1as= 1.8 TeV. The fraction of light B mesons that are produced as L= 1B** states is measured to be 0.28\ub10.06(stat)\ub10.03(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 \ub10.02GeV/c2
