The fraction of chi(c1) and chi(c2) decays in the prompt J=psi yield, F-chi c -> J=psi = sigma(chi c) -> J=psi/ sigma(J/ psi) , is measured by the LHCb detector in pPb collisions at root s(NN) = 8.16 TeV. The study covers the forward (1.5 < y* < 4.0) and sNN backward (-5.0 < y* < -2.5) rapidity regions, where y* is the J=psi rapidity in the nucleon -nucleon centerof -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 presented as a function of the J=psi transverse momentum pT;J/ psi in the range 1 < pT -> J/ psi < 20 GeV=c. The F-chi c -> J=psi fraction at forward rapidity is compatible with the LHCb measurement performed in pp collisions at root s= 7 TeV, whereas the result at s backward rapidity is 2.4 sigma larger than in the forward region for 1 < pT,(J/ psi) < 3 GeV/ c. The increase of F-chi c -> J/ psi at low pT;J/ psi at backward rapidity is compatible with the suppression of the psi(2S) contribution to the prompt J/ psi yield. The lack of in -medium dissociation of chi(c) states observed in this study sets an upper limit of 180 MeV on the free energy available in these pPb collisions to dissociate or inhibit charmonium state formation.