The production of the prompt charm mesons D0, D+, D∗+, and their antiparticles, was measured with the ALICE detector in Pb-Pb collisions at the LHC, at a centre-of-mass energy √sNN = 2.76 TeV per nucleon-nucleon collision. The pt-differential production yields in the range 2<pt<16 GeV/c at central rapidity, |y|<0.5, were used to calculate the nuclear modification factor RAA with respect to a proton-proton reference obtained from the cross section measured at √s = 7 TeV and scaled to √s = 2.76 TeV. For the three meson species, RAA shows a suppression by a factor 3–4, for transverse momenta larger than 5 GeV/c in the 20% most central collisions. The suppression is reduced for peripheral collisions.