  A search for the rare leptonic decay $B^{+} \rightarrow
{\mu}^{+}{\mu}^{-}{\mu}^{+}{\nu}_{{\mu}}$ is performed using proton-proton
collision data corresponding to an integrated luminosity of $4.7$ fb$^{-1}$
collected by the LHCb experiment. The search is carried out in the region where
the lowest of the two ${\mu}^{+}{\mu}^{-}$ mass combinations is below
$980$MeV/c$^{2}$. The data are consistent with the background-only hypothesis
and an upper limit of $1.6 \times 10^{-8}$ at 95% confidence level is set on
the branching fraction in the stated kinematic region.
