Single W boson production in electron–positron collisions is studied with the L3 detector at centre-of-mass energies between 192 GeV and 209 GeV. Events with two acoplanar hadronic jets or a single energetic lepton are selected, and the single W cross section is measured. Combining the results with measurements at lower centre-of-mass energies, the ratio of the measured cross section to the Standard Model expectation is found to be 1.12+0.11−0.10± 0.03. From all single W data, the WWγ gauge coupling parameter κγ is measured to be 1.116+0.082−0.086± 0.068.