The production yields of ϒ(1S), ϒ(2S), and ϒ(3S) quarkonium states are measured through their decays into muon pairs in the CMS detector, in PbPb and pp collisions at the centre-of-mass energy per nucleon pair of 2.76 TeV. The data correspond to integrated luminosities of and for PbPb and pp collisions, respectively. Differential production cross sections are reported as functions of ϒ rapidity y up to 2.4, and transverse momentum up to . A strong centrality-dependent suppression is observed in PbPb relative to pp collisions, by factors of up to ≈2 and 8, for the ϒ(1S) and ϒ(2S) states, respectively. No significant dependence of this suppression is observed as a function of y or . The ϒ(3S) state is not observed in PbPb collisions, which corresponds to a suppression for the centrality-integrated data by at least a factor of ≈7 at a 95% confidence level. The observed suppression is in agreement with theoretical scenarios modeling the sequential melting of quarkonium states in a quark gluon plasma.