  At the electron-proton collider HERA the inclusive $D^{*\pm}$ meson
photoproduction cross section has been measured with the H1 detector in two
different, but partly overlapping, kinematical regions. For the first, where
$<W_{\gamma p}> \approx 200$ GeV and $Q^2 < 0.01 \gev^2$, the result is
$\sigma(\gamma p \to c \bar{c} X) = (13.2 \pm 2.2 ^{+2.1}_{-1.7}
^{+9.9}_{-4.8}) \mu b$. The second measurement for $Q^2 < 4 \gev^2$ yields
$\sigma(\gamma p \to c \bar{c} X) = (9.3 \pm 2.1 ^{+1.9}_{-1.8} ^{+6.9}_
{-3.2}) \mu b$ at $<W_{\gamma p}> \approx 142$ GeV and $\sigma(\gamma p \to c
\bar{c} X) = (20.6 \pm 5.5 ^ {+4.3}_{-3.9} ^{+15.4}_{-7.2}) \mu b$ at
$<W_{\gamma p} > \approx 230$ GeV, respectively. The third error accounts for
an additional uncertainty due to the proton and photon parton density
parametrizations. Differential cross sections are presented as a function of
the $D^{*\pm}$ transverse momentum and rapidity. The results compare reasonably
well with next-to-leading order QCD calculations. Evidence for diffractive
photoproduction of charm quark is presented.
