Inclusive J/ψ production in photon–photon collisions has been observed at LEP II beam energies. A clear signal from the reaction γγ→J/ψ+X is seen. The number of observed N(J/ψ→μ+μ−) events is 36±7 for an integrated luminosity of 617 pb−1, yielding a cross-section of σ(J/ψ+X)=45±9(stat)±17(syst) pb. Based on a study of the event shapes of different types of γγ processes in the PYTHIA program, we conclude that (74±22)% of the observed J/ψ events are due to ‘resolved’ photons, the dominant contribution of which is most probably due to the gluon content of the photon.