This thesis reports the results of a search for the flavor changing neutral current decay of the top quark, t → Zq, in decays of tt pairs produced in pp collisions at a center-of-mass energy of 1.96 TeV. This search is performed on a data sample recorded by the Collider Detector at Fermilab (CDF), corresponding to an integrated luminosity of 1.9 fb-1.;This search follows a previous CDF analysis that resulted in an upper limit for the branching fraction B (t → Zq) of 10.4% at 95% C.L. using a dataset equivalent to 1.1 fb-1 of integrated luminosity. This thesis extends to 1.9 fb-1 of data, and has improved sensitivity to the small signal with the introduction of a template fit technique that includes systematic uncertainties by a linear interpolation between templates. Using a Feldman-Cousins construction, an upper limit at 95% C.L. is set on B (t → Zq) of 3.7%, with the expected upper limit in absence of a signal is 5.0 +/- 2.2% for a top mass of 175 GeV/c2. |