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We report on the measurement of the inclusive Υ (1S) production in Pb–Pb collisions at √sNN = 2.76 TeV carried out at forward rapidity (2.5 < y < 4) and down to zero transverse momentum using its μ+μ−decay channel with the ALICE detector at the Large Hadron Collider. A strong suppression of the inclusive Υ (1S) yield is observed with respect to pp collisions scaled by the number of independent nucleon–nucleon collisions. The nuclear modification factor, for events in the 0–90% centrality range, amounts to 0.30 ± 0.05(stat) ± 0.04(syst). The observed Υ (1S) suppression tends to increase with the centrality of the collision and seems more pronounced than in corresponding mid-rapidity measurements. Our results are compared with model calculations, which are found to underestimate the measured suppression and fail to reproduce its rapidity dependence.