A search is presented for narrow heavy resonances decaying to a top quark and a bottom quark using data collected by the CMS experiment at s=13TeV in 2016. The data set analyzed corresponds to an integrated luminosity of 35.9fb−1 . Final states that include a single lepton (e, μ), multiple jets, and missing transverse momentum are analyzed. No evidence is found for the production of a W′ boson, and the production of right-handed W′ bosons is excluded at 95% confidence level for masses up to 3.6TeV depending on the scenario considered. Exclusion limits for W′ bosons are also presented as a function of their coupling strength to left- and right-handed fermions. These limits on a W′ boson decaying via a top and a bottom quark are the most stringent published to date.