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 $\langle W_{\gamma p}\rangle \approx 200$\ GeV and $Q~2 < 0.01\,\gev~2$, the result is $\sigma(\gamma p \rightarrow c \bar{c} X) = (13.2 \pm 2.2 ~{+2.1}_{-1.7}\, ~{+9.9}_{-4.8})\,\mu b$. The second measurement for $Q~2 < 4\,\gev~2$ yields $\sigma(\gamma p \rightarrow c \bar{c} X) = ( 9.3 \pm 2.1 ~{+1.9}_{-1.8}\, ~{+6.9}_ {-3.2} )\,\mu b$ at $\langle W_{\gamma p}\rangle \approx 142$\,GeV and $\sigma(\gamma p \rightarrow c \bar{c} X) = ( 20.6 \pm 5.5 ~ {+4.3}_{-3.9}\, ~{+15.4}_{-7.2})\,\mu b$ at $\langle W_{\gamma p} \rangle \approx 230$\,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.
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Second systematical errors are due to the dependence on the parton density parametrizations. Tagged events.