A search for single-top production, /ep-->etX, has been made with the ZEUS detector at HERA using an integrated luminosity of 130.1pb-1. Events from both the leptonic and hadronic decay channels of the /W boson resulting from the decay of the top quark were sought. For the leptonic mode, the search was made for events with isolated high-energy leptons and significant missing transverse momentum. For the hadronic decay mode, three-jet events in which two of the jets had an invariant mass consistent with that of the /W were selected. No evidence for top production was found. The results are used to constrain single-top production via flavour-changing neutral current (FCNC) transitions. The ZEUS limit excludes a substantial region in the FCNC /tuγ coupling not ruled out by other experiments.