Submitted to Physical Review Letters ; see paper for full list of authorsThe suppression of the individual Upsilon(nS) states in PbPb collisions with respect to their yields in pp data has been measured. The PbPb and pp datasets used in the analysis correspond to integrated luminosities of 150 inverse microbarns and 230 inverse nanobarns, respectively, collected in 2011 by the CMS experiment at the LHC, at a center-of-mass energy per nucleon pair of 2.76 TeV. The Upsilon(nS) yields are measured from the dimuon invariant mass spectra. The suppression of the Upsilon(nS) yields in PbPb relative to the yields in pp scaled by the number of nucleon-nucleon collisions, R[AA], is measured as a function of the collision centrality. Integrated over c...