  For top-quarks produced via the subprocess $q\bar q\to t\bar t$, the
longitudinal t-quark polarization ($P_{\parallel}$) vanishes in QCD.
$P_{\parallel}$ can be measured by the angular distribution of the lepton in
$t$-quark semileptonic decay. New physics contributions that are parity
nonconserving will be manifest by non-vanishing $P_{\parallel}$, which may be
large. We illustrate this with the s-channel exchange of a massive $X$-gluon
with chiral quark couplings.
