In the supersymmetry (SUSY) models, because of the mass difference bet
ween the left-and right-top squarks, the supersymmetric QCD interactio
ns can generate parity violating effects in the production of tt pairs
. We show that SUSY QCD radiative corrections to the parity violating
asymmetry in the production rates of the left-and right-handed top qua
rks via the q (q) over bar --> t (t) over bar process can reach about
3% at the Fermilab Tevatron with root s = 2TeV. This could be observab
le with an integrated luminosity larger than 2fb(-1). We also show tha
t in these models the SUSY QCD radiative corrections to the tit produc
tion rate are small unless gluinos are very light, of the order of 1 G
eV. (C) 1998 Published by Elsevier Science B.V.