Experimental evidence for the existence of orbitally excited B meson s
tates is presented in an analysis of the B pi and Bpi distribution of
Q = m(B*) - m(B(*)) - m(pi) using Z(0) decay data taken with the DEL
PHI detector at LEP. The mean Q-value of the decays B* --> B(*)pi is
measured to be 284 +/-5 (stat.) +/- 15 (syst.) MeV/c(2), and the Gauss
ian width of the signal is 79 +/- 5 (stat.) +/- 8 (syst) MeV/c(2). Thi
s signal can be described as a single resonance of mass m = 5732+/-5 (
stat.) +/- 20(syst.) MeV/c(2) and full width Gamma = 145 +/- 28 MeV/c(
2). The observed shape is also consistent with the production of sever
al broad and narrow states as predicted by the quark model and partly
observed in the D-meson sector. The production rate of B* per b-jet i
s found to be 0.27 +/- 0.02(stat.) +/- 0.06 (syst.).