The first observation of Z boson production in proton-lead collisions at a centre-of-mass energy per proton-nucleon pair of √sNN = 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 in the direction of the proton beam and in the direction of the lead beam, where the first uncertainty is statistical and the second systematic.