We measure the relative rate of production of orbitally excited (L = 1) sta
tes of B mesons (B**) by observing their decays into B pi (+/-). We reconst
ruct B mesons through semileptonic decay channels using data collected in p
(p) over bar collisions at roots = 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(B-1) = 5.71 +/- 0.02 GeV/c(2).