  The first measurement of the effective lifetime of the $\bar{B}_s^0$ meson in
the decay $\bar{B}_s^0\to D_s^-D_s^+$ is reported using a proton-proton
collision dataset, corresponding to an integrated luminosity of 3 fb$^{-1}$,
collected by the LHCb experiment. The measured value of the $\bar{B}_s^0\to
D_s^-D_s^+$ effective lifetime is $1.379\pm0.026\pm0.017$ ps, where the
uncertainties are statistical and systematic, respectively. This lifetime
translates into a measurement of the decay width of the light $\bar{B}_s^0$
mass eigenstate of \Gamma_L$=0.725\pm0.014\pm0.009$ ps$^{-1}$. The
$\bar{B}_s^0$ lifetime is also measured using the flavor-specific
$\bar{B}_s^0\to D^-D_s^+$ decay to be $1.52\pm0.15\pm0.01 {\rm ps}$.
