We consider a non-universal Z′ that affects primarily the third generation fermions as an example of new physics associated with the top-quark. We first discuss constraints on the mass and coupling strength of such a Z′. We then turn our attention to the flavor changing neutral currents (FCNC) present in the model. We discuss the experimental constraints and their implications. We propose an ansatz to understand the smallness of the FCNC in terms of the CKM matrix.