A search for single top quark production is performed in e ±p collisions at HERA. The search exploits data corresponding to an integrated luminosity of 118.3 pb-1. A model for the anomalous production of top quarks in a flavour changing neutral current process involving a tuγ coupling is investigated. Decays of top quarks into a b quark and a W boson are considered in the leptonic and the hadronic decay channels of the W. Both a cut-based analysis and a multivariate likelihood analysis are performed to discriminate anomalous top quark production from Standard Model background processes. In the leptonic channel, 5 events are found while 1.31 ± 0.22 events are expected from the Standard Model background. In the hadronic channel, no excess above the expectation for Standard Model processes is found. These observations lead to a cross section σ (ep → etX) = 0.29-0.14+0.15 pb at 97 √s = 319 GeV. Alternatively, assuming that the observed events are due to a statistical fluctuation, upper limits of 0.55 pb on the anomalous top production cross section and of 0.27 on the tuγ coupling κ tuγ are established at the 95% confidence level.