  We have searched for signatures of polarization in hadronic jets from $Z^0
\to q \bar{q}$ decays using the ``jet handedness'' method. The polar angle
asymmetry induced by the high SLC electron-beam polarization was used to
separate quark jets from antiquark jets, expected to be left- and
right-polarized, respectively. We find no evidence for jet handedness in our
global sample or in a sample of light quark jets and we set upper limits at the
95% C.L. of 0.063 and 0.099 respectively on the magnitude of the analyzing
power of the method proposed by Efremov {\it et al.}
