  We study $t \bar t$ production in R-parity violating supersymmetry. The
annihilation channel $q \bar q \rightarrow t \bar t$ gets new contributions
from $t$-channel exchange of squarks or sleptons. With the data from Tevatron
on $t \bar t$ production, we find that the squark- or slepton-exchange
processes constrain the $B$-violating $\lambda''$ couplings or the
$L$-violating $\lambda'$ couplings, respectively. Our bounds are already
comparable to the few existing constraints on third-generation $R$-parity
violating couplings, and will improve when more precise measurements of the $t
\bar t$ production cross-section become available. We also discuss the effects
of these couplings for top production at the LHC.
