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 166 μb(^{−1}) and 5.4 pb(^{−1}) 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 (p_T) up to 20GeV/c. 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 (p_T). 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.