This study contains the first realistic estimate for the CMS/LHC sensitivity to Flavour Changing Neutral Currents (FCNC) in the top quark sector. The non-Standard Model decays t→Zq and t→ γ q (where q = u, c) have been studied at √s = 14 TeV exploiting the leptonic decays of the Z⁰ boson and the photon. A realistic detector simulation has been used and the most important 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→ γ q)= 5.7 x 10⁻⁴, allowing some models of new physics to be tested.