A first flavor-tagged measurement of the time-dependent CP-violating asymmetry in B0s→ϕϕ decays is presented. In this decay channel, the CP-violating weak phase arises due to CP violation in the interference between B0s-B¯¯¯0s mixing and the b→ss¯s 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 B0s→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%.