Using a proton–proton collision data sample collected by the LHCb detector and corresponding to an integrated luminosity of 5.7~text {fb}^{-1}, the lifetime of the light {{B} ^0_{s}} mass eigenstate, tau _{L}, is measured using the B^0_s rightarrow J/psi eta decay mode to be τL=1.445±0.016(stat)±0.008(syst)ps.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \ au _{\ ext {L}} = 1.445 \\pm 0.016 \ ext {(stat)} \\pm 0.008 \ ext {(syst)} \\,\ ext {ps}. \\end{aligned}$$\\end{document}A combination of this result with a previous LHCb analysis using an independent dataset corresponding to 3 fb^{-1} of integrated luminosity gives τL=1.452±0.014±0.007±0.002ps,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \ au _{\ ext {L}} = 1.452 \\pm 0.014 \\pm 0.007 \\pm 0.002 \\,\ ext {ps}, \\end{aligned}$$\\end{document}where the first uncertainty is statistical, the second due to the uncorrelated part of the systematic uncertainty and the third due to the correlated part of the systematic uncertainty.