A first flavor-tagged measurement of the time-dependent CP-violating asymmetry in B-s(0) -> phi phi decays is presented. In this decay channel, the CP-violating weak phase arises due to CP violation in the interference between B-s(0)-(B) over bar (0)(s) mixing and the b -> s (s) over bars gluonic penguin decay amplitude. Using a sample of pp collision data corresponding to an integrated luminosity of 1.0 fb(-1) and collected at a center-of-mass energy of 7 TeV with the LHCb detector, 880 B-s(0) -> phi phi signal decays are obtained. The CP-violating phase is measured to be in the interval [-2.46, -0.76] rad at a 68% confidence level. The p value of the standard model prediction is 16%.