The fraction of χ_{c1} and χ_{c2} decays in the prompt J/ψ yield, F_{χ_{c}→J/ψ}=σ_{χ_{c}→J/ψ}/σ_{J/ψ}, is measured by the LHCb detector in pPb collisions at sqrt[s_{NN}]=8.16 TeV. The study covers the forward (1.5<y^{*}<4.0) and backward (-5.0<y^{*}<-2.5) rapidity regions, where y^{*} is the J/ψ rapidity in the nucleon-nucleon center-of-mass system. Forward and backward rapidity samples correspond to integrated luminosities of 13.6±0.3 and 20.8±0.5 nb^{-1}, respectively. The result is …