The ATLAS experiment has observed 1995 $Z$ boson candidates in data corresponding to $0.15\text{ }\text{ }{\mathrm{nb}}^{\ensuremath{-}1}$ of integrated luminosity obtained in the 2011 LHC $\mathrm{Pb}+\mathrm{Pb}$ run at $\sqrt{{s}_{NN}}=2.76\text{ }\text{ }\mathrm{TeV}$. 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.