The first search for the rare radiative decay Ξ − b → Ξ − γ is performed using data collected by the LHCb experiment in proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4 fb −1 . The Ξ − b → Ξ − J/ψ channel is used as normalization. No Ξ − b → Ξ − γ signal is found and an upper limit of B(Ξ − b → Ξ − γ) < 1.3 × 10 −4 at 95% confidence level is obtained.