A time-dependent analysis of the B-s(0) -> phi gamma decay rate is performed to determine the CP -violating observables S-phi gamma and C-phi gamma and the mixing-induced observable A(phi gamma)(Delta). The measurement is based on a sample of pp collision data recorded with the LHCb detector, corresponding to an integrated luminosity of 3 fb(-1) at center-of-mass energies of 7 and 8 TeV. The measured values are S-phi gamma = 0.43 +/- 0.30 +/- 0.11, C-phi gamma = 0.11 +/- 0.29 +/- 0.11, and A(phi gamma)(Delta) = -0.67(-0.41)(+0.37) +/- 0.17, where the first uncertainty is statistical and the second systematic. This is the first measurement of the observables S and C in radiative B-s(0) decays. The results are consistent with the standard model predictions.
