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