The Λb0→Λφ decay is observed using data corresponding to an integrated luminosity of 3.0 fb-1 recorded by the LHCb experiment. The decay proceeds at leading order via a b→sss 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±1.04±0.35-0.62+0.67)×10-6, 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.