  Inclusive production of $\mathrm{D^{*\pm}}$ mesons in two-photon collisions
was measured by the L3 experiment at LEP. The data were collected at a
centre-of-mass energy $\sqrt{s} = 189$ GeV with an integrated luminosity of
$176.4 \mathrm{pb^{-1}}$. Differential cross sections of the process
$\mathrm{e^+e^- \to D^{*\pm} X}$ are determined as functions of the transverse
momentum and pseudorapidity of the $\mathrm{D^{*\pm}}$ mesons in the kinematic
region 1 GeV $< p_{T}^{\mathrm{D^*}} < 5 $ GeV and $\mathrm{|\eta^{D^*}|} <
1.4$. The cross section integrated over this phase space domain is measured to
be $132 \pm 22(stat.) \pm 26(syst.)$ pb. The differential cross sections are
compared with next-to-leading order perturbative QCD calculations.
