(1) University of Glasgow, Kelvin Building, Glasgow G12 8QQ, Scotland.
The potential of the LHCb experiment to make the first discovery of a two-body charmless baryonic $B$ decay is explored. The most promising channel is $B^0 \rightarrow p \bar{p}$, for which a 5$\sigma$ discovery is possible with around 0.25 $\text{fb}^{-1}$ of LHCb data at nominal centre-of-mass energy, assuming that the value for the $B^0 \rightarrow p \bar{p}\,$ branching ratio is close to the current experimental upper limit. LHCb also has prospects for other two-body charmless baryonic $B$ decays, such as $B_s \rightarrow p \bar{p}$ and decays involving a $\Lambda$.