The radiative decay Lambda(0 )(b)-> Lambda gamma is observed for the first time using a data sample of proton-proton collisions corresponding to an integrated luminosity of 1.7 fb(-1) collected by the LHCb experiment at a center-of-mass energy of 13 TeV. Its branching fraction is measured exploiting the B-0 -> K*(0)gamma decay as a normalization mode and is found to be B(Lambda(0 )(b)-> Lambda gamma) = (7.1 +/- 1.5 +/- 0.6 +/- 0.7) x 10(-6), where the quoted uncertainties arc statistical, systematic, and systematic from external inputs, respectively. This is the first observation of a radiative decay of a beauty baryon.