We report a search for the flavor-changing neutral-current decay of the top quark t-->Zq (q=u, c) in pp collisions at sqrt[s]=1.96 TeV using a data sample corresponding to an integrated luminosity of 1.9 fb(-1) collected by the CDF II detector. This decay is strongly suppressed in the standard model and an observation of a signal at the Fermilab Tevatron would be an indication of physics beyond the standard model. Using Z+ > or = 4 jet final state candidate events, with and without an identified bottom quark jet, we obtain an upper limit of B(t-->Zq) < 3.7% at 95% C.L.
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