We search for the Flavor-Changing Neutral Current decays of the top quark t -> q gamma and t -> qZ (here q represents the c and u quarks) in pbar p collisions at sqrt s = 1.8 TeV from a dataset with an integrated luminosity of approximately 110 pb^-1 collected during the 1992-1995 run of the Collider Detector at Fermilab. We set limits on the branching fractions BF(t -> q gamma) < 2.9% (at 95% CL) and BF(t -> qZ) < 44% (at 90% CL), consistent with the Standard Model.