Abstract: The Lambda(0)(b) -> Lambda phi 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 -> s<(s)double over bar>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 +/- 1.04 +/- 0.35(-0.62)(+0.67)) x 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.