The inclusive production of D * ± mesons in two-photon collisions is measured with the ALEPH detector at e + e − centre-of-mass energies from 183 GeV to 209 GeV. A total of 360 ± 27 D * ± meson events were observed from an integrated luminosity of 699 pb −1 . Contributions from direct and single-resolved processes are separated using the ratio of the transverse momentum p D * ± t of the D * ± to the visible invariant mass W vis of the event. Differential cross sections of D * ± production as functions of p D * ± t and the pseudorapidity |η D * ± | are measured in the range 2 GeV/c < p D * ± t < 12 GeV/c and |η D * ± | < 1.5. They are compared to next-to-leading order (NLO) perturbative QCD calculations. The extrapolation of the integrated visible D * ± cross section to the total charm cross section, based on the Pythia Monte Carlo program, yields σ(e + e − → e + e − cc) < √ s>=197 GeV = 731 ± 74 stat ± 47 syst ± 157 extr pb.