The ATLAS experiment has observed 1995 Z boson candidates in data corresponding to 0.15 nb(-1) of integrated luminosity obtained in the 2011 LHC Pb+Pb run at sqrt[s(NN)]=2.76 TeV. The Z bosons are reconstructed via dielectron and dimuon decay channels, with a background contamination of less than 3%. Results from the two channels are consistent and are combined. Within the statistical and systematic uncertainties, the per-event Z boson yield is proportional to the number of binary collisions estimated by the Glauber model. The elliptic anisotropy of the azimuthal distribution of the Z boson with respect to the event plane is found to be consistent with zero.