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The ALICE experiment has measured the inclusive J/psi production in Pb-Pb collisions at sqrt(sNN) = 2.76 TeV down to pt = 0 in the rapidity range 2.5 < y < 4. A suppression of the inclusive J/psi yield in Pb-Pb is observed with respect to the one measured in pp collisions scaled by the number of binary nucleon-nucleon collisions. The nuclear modification factor, integrated over the 0%-80% most central collisions, is 0.545 +/- 0.032 (stat.) +/- 0.084 (syst.) and does not exhibit a significant dependence on the collision centrality. These features appear significantly different from lower energy measurements. Models including J/psi production from charm quarks in a deconfined partonic phase can describe our data.