The production of charm quarks is studied in deep-inelastic
electron-photon scattering using data recorded by the OPAL detector at LEP
at nominal e$^+$e$^-$ centre-of-mass energies from 183 to 209 GeV. The charm
quarks have been identified by full reconstruction of charged D$^*$ mesons
using their decays into D$^0\pi$ with the D$^0$ observed in two decay 
modes with
charged particle final states, K$\pi$ and K$\pi\pi\pi$.  The inclusive
cross-section for charged D$^*$ production in the reaction 
e$^+$e$^- \rightarrow \mathrm e^+\mathrm e^- \mathrm D^* X$
is determined in the region $0.0014 < x < 0.87$ and 
$5 < Q^2 < 100$~GeV$^2$. For $x > 0.1$ the perturbative QCD 
calculation at next-to-leading order perfectly agrees with the
measured cross section. For $x < 0.1$ the measured cross section
is $43.8 \pm 14.3 \pm 6.3 \pm 2.8$~pb with a next-to-leading
order prediction of $17.0~^{+2.9}_{-2.3}$~pb.