The radiative decay Λ0b→Λγ 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 B0→K*0γ decay as a normalization mode and is found to be B(Λ0b→Λγ)=(7.1±1.5±0.6±0.7)×10−6, where the quoted uncertainties are statistical, systematic, and systematic from external inputs, respectively. This is the first observation of a radiative decay of a beauty baryon.