Abstract: The first observation of Z boson production in proton-lead collisions at a centre-of-mass energy per proton-nucleon pair of root(s) N N = 5TeV is presented. The data sample corresponds to an integrated luminosity of 1.6 nb(-1) collected with the LHCb detector. The Z candidates are reconstructed from pairs of oppositely charged muons with pseudorapidities between 2.0 and 4.5 and transverse momenta above 20 GeV/c. The invariant dimuon mass is restricted to the range 60-120 GeV/c. The Z production cross-section is measured to be sigma(Z ->mu+mu-) (fwd) = 13.5(-4.0)(+5.4)(stat.) +/- 1.2(syst.) nb in the direction of the proton beam and sigma(Z ->mu+mu-) (bwd) = 10.7(-5.1)(+8.4)(stat.) +/- 1.0(syst.) nb in the direction of the lead beam, where the first uncertainty is statistical and the second systematic.