Jet production in PbPb collisions at a nucleon-nucleon center-of-mass energy of 2.76 TeV was studied with the CMS detector at the LHC, using a data sample corresponding to an integrated luminosity of 6.7 inverse microbarns. Jets are reconstructed using the energy deposited in the CMS calorimeters and studied as a function of collision centrality. With increasing collision centrality, a striking imbalance in dijet transverse momentum is observed, consistent with jet quenching. The observed effect extends from the lower cut-off used in this study (jet transverse momentum = 120 GeV/c) up to the statistical limit of the available data sample (jet transverse momentum approximately 210 GeV/c). Correlations of charged particle tracks with jets indicate that the momentum imbalance is accompanied by a softening of the fragmentation pattern of the second most energetic, away-side jet. The dijet momentum balance is recovered when integrating low transverse momentum particles distributed over a wide angular range relative to the direction of the away-side jet.