A first flavour-tagged measurement of the time-dependent CP-violating asymmetry in $B_s^0 to phiphi$ decays is presented. In this decay channel, the CP-violating weak phase arises due to CP violation in the interference between $B_s^0$-$bar{B}_s^0$ mixing and the $b to s bar{s} 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 centre-of-mass energy of $7 rm TeV$ with the LHCb detector, $880 B_s^0 to phiphi$ signal decays are obtained. The CP-violating phase is measured to be in the interval [-2.46, -0.76] rm rad$ at 68% confidence level. The p-value of the Standard Model prediction is 16%.