The first measurement of the effective lifetime of the (B) over bar (o)(s) meson in the decay (B) over bar (o)(s) -> D-s(-) D-s(+) is reported using a proton-proton collision data set, corresponding to an integrated luminosity of 3 fb(-1), collected by the LHCb experiment. The measured value of the (B) over bar (o)(s) -> D-s(-) D-s(+) effective lifetime is 1.379 +/- 0.026 +/- 0.017 ps, where the uncertainties are statistical and systematic, respectively. This lifetime translates into a measurement of the decay width of the light (B) over bar (o)(s) mass eigenstate of Gamma(L) 0.725 +/- 0.014 +/- 0.009 ps(-1). The (B) over bar (o)(s) lifetime is also measured using the flavor-specific (B) over bar (o)(s) -> D- D-s(+) decay to be 1.52 +/- 0.15 +/- 0.01 ps.