The polarization of Lambda baryons from Z decays is studied with the A
LEPH apparatus. Evidence of longitudinal polarization of s quarks from
Z decay is observed for the first time. The measured longitudinal Lam
bda polarization is P-L(Lambda) = -0.32 +/- 0.07 for z = p/pbeam > 0.3
. This agrees with the prediction of -0.39 +/- 0.08 from the standard
model and the constituent quark model, where the error is due to uncer
tainties in the mechanism for Lambda production. The observed Lambda p
olarization is diluted with respect to the primary s quark polarizatio
n by Lambda baryons without a primary s quark. Measurements of the Lam
bda forward-backward asymmetry and of the correlation between back-to-
back Lambda<(Lambda)over bar> pairs are used to check this dilution. I
n addition the transverse Lambda polarization is measured. An indicati
on of transverse polarization, more than two standard deviations away
from zero, is found along the normal to the plane defined by the thrus
t axis and the Lambda direction.