The first study of W boson production in pPb collisions is presented, for bosons decaying to a muon or electron, and a neutrino. The measurements are based on a data sample corresponding to an integrated luminosity of 34.6 nb(^{-1}) at a nucleonânucleon centre-of-mass energy of (\sqrt{s_{\mathrm{NN}}})= 5.02 TeV, collected by the CMS experiment. The W boson differential cross sections, lepton charge asymmetry, and forward-backward asymmetries are measured for leptons of transverse momentum exceeding 25 GeV/(c), and as a function of the lepton pseudorapidity in the |(\eta_{lab})| < 2.4 range. Deviations from the expectations based on currently available parton distribution functions are observed, showing the need for including W boson data in nuclear parton distribution global fits.