This thesis describes a measurement of the average proper decay time of the B_c mesons, the ground state of bottom and charm quark bound states. The lifetime measurement is carried out in the decay modes B_c->J/psi+e+X and B_c->J/psi+mu+X, where the J/psi decays as J/psi->mu^+mu^- and the X are unmeasured particles such as nu_e or nu_mu. The data are collect by the CDF II detector which measures the properties of particles created in sqrt(s)=1.96 TeV pp-bar collisions delivered by the Fermilab Tevatron. This measurement uses ~1 fb^-1 of integrated luminosity. The measured average proper decay time of B_c mesons, tau = 0.475^{+0.053}_{-0.049}(stat.) +/-0.018(syst.) ps, is competitive with the most precise measurements in the world and confirms previous measurements and theoretical predictions. Posted to /cdf/www/pub/thesis/cdf9657_bclt_jpsil_thesis.pdf http://www-cdf.fnal.gov/thesis/cdf9657_bclt_jpsil_thesis.pdf Posted by mhartz