The suppression of the individual Υ(nS) states in PbPb collisions with respect to their yields in pp data has been measured. The PbPb and pp data sets used in the analysis correspond to integrated luminosities of 150 μb-1 and 230 nb-1, 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 Υ(nS) yields are measured from the dimuon invariant mass spectra. The suppression of the Υ(nS) yields in PbPb relative to the yields in pp, scaled by the number of nucleon-nucleon collisions, RAA, is measured as a function of the collision centrality. Integrated over centrality, the RAA values are 0.56±0.08(stat)±0.07(syst), 0.12±0.04(stat)±0.02(syst), and lower than 0.10 (at 95% confidence level), for the Υ(1S), Υ(2S), and Υ(3S) states, respectively. The results demonstrate the sequential suppression of the Υ(nS) states in PbPb collisions at LHC energies.