  We report a measurement of the Lambda_b lifetime in the exclusive decay
Lambda_b --> J/psi Lambda0 in p-pbar collisions at sqrt(s) = 1.96 TeV using an
integrated luminosity of 1.0 fb^{-1} of data collected by the CDF II detector
at the Fermilab Tevatron. Using fully reconstructed decays, we measure
tau(Lambda_b) = 1.593 ^{+0.083}_{-0.078} (stat.) +- 0.033 (syst.) ps. This is
the single most precise measurement of tau(Lambda_b) and is 3.2 sigma higher
than the current world average.
