The first measurement of inclusive D(s)(±) photoproduction at HERA has been performed with the ZEUS detector for photon-proton centre-of-mass energies 130 < W < 280GeV. The measured cross section for 3 < p (is perpendicular to)/(D(s)) < 12GeV and |η(D(s))| < 1.5 is σ(ep → D(s)X) = 3.79 ± 0.59(stat.) -0.46/+0.26 (syst.) ± 0.94(br.)nb, where the last error arises from the uncertainty in the D(s)(±) decay branching ratio. The measurements are compared with inclusive D*(±) photoproduction cross sections in the same kinematic region and with QCD calculations. The D(s)(±) cross sections lie above a fixed-order next-to-leading order calculation and agree better with a tree-level O(αα(s)/3) calculation that was tuned to describe the ZEUS D*(±) cross sections. The ratio of D(s)(±) to D*(±) cross sections is 0.41 ± 0.07 (stat.) -0.05/+0.03 (syst.) ± 0.10(br.). From this ratio, the strangeness-suppression factor in charm photoproduction, within the LUND string fragmentation model, has been calculated to be γ(s) = 0.27 ± 0.05 ± 0.07(br.). The cross-section ratio and γ(s) are in good agreement with those obtained in charm production in e+e- annihilation. (C) 2000 Elsevier Science B.V.