In the Standard Model, b quarks produced in e(+)e(-) annihilation at the Z(
0) peak have a large average longitudinal polarization of -0.94. Some fract
ion of this polarization is expected to be transferred to b-flavored baryon
s during hadronization. The average longitudinal polarization of weakly dec
aying b baryons, [P-L(Lambda b)], is measured in approximately 4.3 million
hadronic Z(0) decays collected with the OPAL detector between 1990 and 1995
at LEP. Those b baryons that decay semileptonically and produce a Lambda b
aryon are identified through the correlation of the baryon number of the La
mbda and the electric charge of the lepton. In this semileptonic decay, the
ratio of the neutrino energy to the lepton energy is a sensitive polarizat
ion observable. The neutrino energy is estimated using missing energy measu
rements. From a fit to the distribution of this ratio, the value [p(L)(Lamb
da b)] = -0.56(-0.13)(+0.20) +/- 0.09 is obtained, where the first error is
statistical and the second systematic. (C) 1998 Elsevier Science B.V. All
rights reserved.