This paper contains the first realistic estimate for the CMS sensitivity to Flavour Changing Neutral Currents (FCNC) in the top quark sector. The non Standard Model decays t -> Zq and t -> gamma q (q represents c or u quarks) have been studied at sqrts = 14 TeV exploiting leptonic decays of the Z boson and the photon. A realistic detector simulation has been adopted and the most relevant systematic effects have been addressed. The 5- sigma discovery limits for the two decays are BR(t-> qZ) =11.4 x 10^ -4 and BR(t -> gamma q ) =5.7 x 10^ -4, allowing some models of new physics to be tested
