A search for pair-produced heavy vectorlike charge-2/3 quarks, T, in pp collisions at a center-of-mass energy of 7 TeV, is performed with the CMS detector at the LHC. Events consistent with the flavor-changing-neutral-current decay of a T quark to a top quark and a Z boson are selected by requiring two leptons from the Z-boson decay, as well as an additional isolated charged lepton. In a data sample corresponding to an integrated luminosity of 1.14 fb(-1), the number of observed events is found to be consistent with the standard model background prediction. Assuming a branching fraction of 100\% for the decay T -> tZ, a T quark with a mass less than 475 GeV/c(2) is excluded at the 95\% confidence level.