A measurement of W boson production in lead-lead collisions at root s(NN) = 2.76 TeV is presented. It is based on the analysis of data collected with the ATLAS detector at the LHC in 2011 corresponding to an integrated luminosity of 0.14 nb(-1) and 0.15 nb(-1) in the muon and electron decay channels, respectively. The differential production yields and lepton charge asymmetry are each measured as a function of the average number of participating nucleons < N-part > and absolute pseudorapidity of the charged lepton. The results are compared to predictions based on next-to-leading-order QCD calculations. These measurements are, in principle, sensitive to possible nuclear modifications to the parton distribution functions and also provide information on scaling of W boson production in multi-nucleon systems.