  Charm production is studied in deep-inelastic electron-photon scattering
using OPAL data at e+e- centre-of-mass energies from 183 to 209 GeV. Charm
quarks are identified by exclusive reconstruction of D* mesons. The
cross-section of D* production is measured in a restricted kinematic region,
and then extrapolated to the total charm production cross-section and the charm
structure function of the photon. For x>0.1 the measurement is well described
by Monte Carlo models and perturbative QCD calculations but for x<0.1 the
predictions are lower than the data both in the directly measured region and
after the extrapolation.
