  We study the charmed baryon production reaction ${\bar p} p \to {\bar
\Lambda}_c^- \Lambda_c^+$ using the $t$-channel $D^0$ and $D^{*0}$ meson
exchange diagrams within an effective Lagrangian model involving the physical
hadron masses and the coupling constants determined from SU(4) flavor symmetry.
The initial and final state distortion effects are accounted for by using a
simple eikonal approximation based procedure. The vertex parameters of our
model have been checked by employing them to calculate the cross sections for
the ${\bar p} p \to {\bar \Lambda} \Lambda$ reaction within a similar model. We
predict the ${\bar \Lambda}_c^- \Lambda_c^+$ production cross sections in the
range of 1-30 $\mu b$ for antiproton beam momenta varying between threshold to
20 GeV/c. The respective roles of $D^0$ and $D^{*0}$ meson exchanges and also
those of the vector and tensor components of the $D^{*0}$ coupling have been
investigated
