The production of Z bosons is studied in the dimuon and dielectron decay channels in PbPb and pp collisions at root s(NN) = 2.76TeV, using data collected by the CMS experiment at the LHC. The PbPb data sample corresponds to an integrated luminosity of about 166 mu b(-1), while the pp data sample collected in 2013 at the same nucleon-nucleon centre-of-mass energy has an integrated luminosity of 5.4 pb(-1). The Z boson yield is measured as a function of rapidity, transverse momentum, and collision centrality. The ratio of PbPb to pp yields, scaled by the number of inelastic nucleon-nucleon collisions, is found to be 1.06 +/- 0.05 (stat) +/- 0.08 (syst) in the dimuon channel and 1.02 +/- 0.08 (stat) +/- 0.15 (syst) in the dielectron channel, for centrality-integrated Z boson production. This binary collision scaling is seen to hold in the entire kinematic region studied, as expected for a colourless probe that is unaffected by the hot and dense QCD medium produced in heavy ion collisions.