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This dissertation describes the measurement of the average B hadron lifetime using a high statistics sample of B-- J/psi X decays produced in proton antiproton collisions at a center of mass energy of 1.8 TeV at the Fermilab Tevatron. The integrated luminosity of the sample is 10.1 pb-1 recorded with the Collider Detector at Fermilab (CDF). In this analysis the decay vertex of the decay J/psi --mu^+ mu^-$ as reconstructed by a silicon vertex detector is used to extract the lifetime from the data. We find the following value for the average b hadron lifetime: [ tau_{B} = 1.46 pm 0.06; (stat.); pm 0.06; (syst.); ps] This is the first measurement of the b-hadron lifetime at a hadron collider. It demonstrates that it is possible to access the large b-quark production cross section in $poverline{p}$ collisions and to achieve high statistics even in modes which have small product branching ratios as in this case: $BR(Brightarrow J/psi X) cdot BR(J/psi rightarrow mu^+ mu^-) = 7.7 times 10^{-4}$.