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. We use a dataset (sum Ldt \sim 110 pb^-1) collected during the 1992-1995 run of the Collider Detector at Fermilab. We set 95% confidence level limits on the branching fractions B(t -> q gamma) < 3.2% and B(t -> qZ) < 33%, consistent with the Standard Model.