Abstract: The photon polarization in b -> s gamma transitions is measured for the first time in radiative b -baryon decays exploiting the unique spin structure of Lambda(0)(b)-> Lambda(gamma) decays. A data sample corresponding to an integrated luminosity of 6 fb(-1) collected by the LHCb experiment in pp collisions at a center-of-mass energy of 13 TeV is used. The photon polarization is measured to be alpha(gamma) = 0.82(-0.26-0.)(13)(+)(0.17+0.04), where the first uncertainty is statistical and the second systematic. This result is in agreement with the Standard Model prediction and previous measurements in b-meson decays. Charge-parity breaking effects are studied for the first time in this observable and found to be consistent with CP symmetry.