Correlations induced by quantum statistics are sensitive to the spatiotemporal extent as well as dynamics of particle-emitting sources in heavy-ion collisions. In addition, such correlations can be used to search for the presence of a coherent component of pion production. Two- and three-pion correlations of same and mixed charge are measured at low relative momentum to estimate the coherent fraction of charged pions in Pb-Pb collisions at sNN=2.76 TeV at the CERN Large Hadron Collider with ALICE. The genuine three-pion quantum statistics correlation is found to be suppressed relative to the two-pion correlation based on the assumption of fully chaotic pion emission. The suppression is observed to decrease with triplet momentum. The observed suppression at low triplet momentum may correspond to a coherent fraction in charged-pion emission of 23%±8%.