Inclusive photoproduction of D*+- in ep collisions at HERA has been measured with the ZEUS detector for photon-proton centre of mass energies in the range 115 < W < 280 GeV and photon virtuality Q**2 < 4 GeV**2. The cross section sigma(ep --> D*X) integrated over the kinematic region pt(D*) > 3 GeV and -1.5 < eta(D*) < 1.0 is (10.6+-1.7(stat.)+1.6(syst.)-1.3(syst.)) nb. Differential cross sections as functions of pt(D*), eta(D*) and W are given. The data are compared with two next-to-leading order perturbative QCD predictions. For a calculation using a massive charm scheme the predicted cross sections are smaller than the measured ones. A recent calculation using a massless charm scheme is in agreement with the data.
18 pages including 4 figures