A search for Z bosons in the mu(+)mu(-) decay channel has been performed in PbPb collisions at root s(NN) = 2.76 TeV with the CMS detector at the LHC, in a 7.2 mu b(-1) data sample. The number of opposite-sign muon pairs observed in the 60-120 GeV/c(2) invariant mass range is 39, corresponding to a yield per unit of rapidity (y) and per minimum bias event of {[}33.8 +/- 5.5(stat) +/- 4.4(syst)] x 10(-8), in the vertical bar y vertical bar < 2.0 range. Rapidity, transverse momentum, and centrality dependencies are also measured. The results agree with next-to-leading order QCD calculations, scaled by the number of incoherent nucleon-nucleon collisions.