  Though not considered in general, purely baryonic decays could shed light on
the puzzle of the baryon number asymmetry in the universe by means of a better
understanding of the baryonic nature of our matter world. As such, they
constitute a yet unexplored class of decay processes worth investigating. We
propose to search for purely baryonic decay processes at the LHCb experiment.
No such type of decay has ever been observed. In particular, we concentrate on
the decay $\Lambda_b^0\to p\bar pn$, which is the simplest purely baryonic
decay mode, with solely spin-1/2 baryons involved. We predict its decay
branching ratio to be ${\cal B}(\Lambda_b^0\to p\bar
pn)=(2.0^{+0.3}_{-0.2})\times 10^{-6}$, which is sufficiently large to make the
decay mode accessible to LHCb. Our study can be extended to other purely
baryonic decays such as $\Lambda_b^0\to p\bar p \Lambda$ and $\Lambda_b^0\to
\Lambda\bar \Lambda\Lambda$, as well as to similar decays of anti-triplet
$b$-baryons such as $\Xi_b^{0,-}$.
