A first flavor-tagged measurement of the time-dependent CP-violating asymmetry in B(s)(0) → ϕϕ 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(s)(0) mixing and the b → sss 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) → ϕϕ 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%.