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The first measurement of the cross sections for D*±-meson diffractive photoproduction was performed with the ZEUS detector at the HERA ep collider by using an integrated luminosity of 38 pb−1. The measurement was performed for photon-proton c.m. energies in the range 130<W<280 GeV and photon virtualities in the region Q 2<1 GeV2. The product D*± mesons were reconstructed for p T D* >2 GeV and −1.5<η D*<1.5 from the decay channel D*+ → D 0 π s + with D 0 → K − π + (+ c.c.). The diffractive component was selected for 0.001 <x P<0.018. The measured cross section in this kinematical range is σep→e′D∗Xp′diff=0.74±0.21(stat.)−0.18+0.27(syst.)±0.16(p.diss.) nb (ZEUS preliminary). The measured integrated and differential cross sections are compared with theoretical expectations.