The first search for the rare radiative decay $Xi_b^- to Xi^- gamma$ 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 $Xi_b- to Xi^- J/psi$ channel is used as normalization. No $Xi_b^- to Xi^- gamma$ signal is found and an upper limit of $mathcal{B}(Xi_b^- to Xi^- gamma) < 1.3 times 10^{-4}$ at 95% confidence level is obtained.
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