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We report on a measurement of $b$-hadron lifetimes in the fully reconstructeddecay modes B^+ -->J/Psi K+, B^0 --> J/Psi K*, B^0 --> J/Psi Ks, and Lambda_b--> J/Psi Lambda using data corresponding to an integrated luminosity of 4.3${\rm fb}^{-1}$, collected by the CDF II detector at the Fermilab Tevatron. Themeasured lifetimes are $\tau$B^+ = $1.639 \pm 0.009 ({\rm stat}) \pm 0.009 {\rm(syst) ~ ps}$, $\tau$B^0 = $1.507 \pm 0.010 ({\rm stat}) \pm 0.008 {\rm (syst)~ ps}$ and $\tau$Lambda_b = $1.537 \pm 0.045 ({\rm stat}) \pm 0.014 {\rm (syst)~ ps}$. The lifetime ratios are $\tau$B^+/$\tau$B^0 = $1.088 \pm 0.009 ({\rmstat})\pm 0.004 ({\rm syst})$ and $\tau$Lambda_b/$\tau$B^0 = $1.020 \pm 0.030({\rm stat})\pm 0.008 ({\rm syst})$. These are the most precise determinationsof these quantities from a single experiment.

Measurement of b hadron lifetimes in exclusive decays containing a J/psi in p-pbar collisions at sqrt(s)=1.96TeV