We present a measurement of the ratio of the B¯s⁰ meson lifetime, in the flavor-specific decay to Ds⁺π⁻, to that of the B¯⁰ meson. The pp collision data used correspond to an integrated luminosity of 1 fb(-1), collected with the LHCb detector, at a center-of-mass energy of 7 TeV. Combining our measured value of 1.010±0.010±0.008 for this ratio with the known B¯⁰ lifetime, we determine the flavor-specific B¯s⁰ lifetime to be τ(B¯s⁰ )=1.535±0.015±0.014 ps, where the uncertainties are statistical and systematic, respectively. This is the most precise measurement to date, and is consistent with previous measurements and theoretical predictions.