  The $\Lambda_b^0\to\Lambda\phi$ decay is observed using data corresponding to
an integrated luminosity of 3.0fb$^{-1}$ recorded by the LHCb experiment. The
decay proceeds at leading order via a $b\to s\bar{s}s$ loop transition and is
therefore sensitive to the possible presence of particles beyond the Standard
Model. A first observation is reported with a significance of $5.9$ standard
deviations. The value of the branching fraction is measured to be
$(5.18\pm1.04\pm0.35\,^{+0.67}_{-0.62})\times10^{-6}$, where the first
uncertainty is statistical, the second is systematic, and the third is related
to external inputs. Triple-product asymmetries are measured to be consistent
with zero.
