The data recorded at a centre-of-mass energy of √s=189 GeV by the OPAL detector at LEP are used to search for trilinear couplings of the neutral gauge bosons in the process e+e−→Zγ. The cross-sections for multihadronic events with an energetic isolated photon, and for events with a high energy photon accompanied by missing energy are measured. These cross-sections and the photon energy, polar angle and isolation angle distributions are compared to the Standard Model predictions and to the theoretical expectations of a model allowing for ZγZ and Zγγ vertices. Since no significant deviations with respect to the Standard Model expectations are found, constraints are derived on the strength of neutral trilinear gauge couplings.