A first flavour-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-Bˉ0s mixing and the b→ssˉs gluonic penguin decay amplitude. Using a sample of pp collision data corresponding to an integrated luminosity of 1.0fb−1 and collected at a centre-of-mass energy of 7TeV 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 68% confidence level. The p-value of the Standard Model prediction is 16%.