  The ratio of the \Lambda b baryon lifetime to that of the B0 meson is
measured using 1.0/fb of integrated luminosity in 7 TeV center-of-mass energy
pp collisions at the LHC. The \Lambda b baryon is observed for the first time
in the decay mode \Lambda b -> J/\psi pK-, while the B0 meson decay used is the
well known B0 -> J/\psi pi+K- mode, where the pi+ K- mass is consistent with
that of the K*0(892) meson. The ratio of lifetimes is measured to be 0.976 +/-
0.012 +/- 0.006, in agreement with theoretical expectations based on the heavy
quark expansion. Using previous determinations of the B0 meson lifetime, the
\Lambda b lifetime is found to be 1.482 +/- 0.018 +/- 0.012 ps. In both cases
the first uncertainty is statistical and the second systematic.
