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