  We measure the forward-backward asymmetry in the production of $\Lambda_b^0$
and $\overline \Lambda_b^0$ baryons as a function of rapidity in $p \overline p
$ collisions at $\sqrt s =1.96$ TeV using $10.4$ fb$^{-1}$ of data collected
with the D0 detector at the Fermilab Tevatron collider. The asymmetry is
determined by the preference of $\Lambda_b^0$ or $\overline \Lambda_b^0$
particles to be produced in the direction of the beam protons or antiprotons,
respectively. The measured asymmetry integrated over rapidity $y$ in the range
$0.1<|y|<2$ is $A=0.04 \pm 0.07 {\rm (stat)} \pm 0.02 {\rm (syst)}$.
