This Letter reports the first measurement of prompt $chi_{c1}$ and $chi_{c2}$ charmonium production in nuclear collisions at Large Hadron Collider energies. The cross-section ratio $sigma(chi_{c2}) / sigma(chi_{c1})$ is measured in $p$Pb collisions at $sqrt{s_{NN}}$ = 8.16 TeV, collected with the LHCb experiment. The $chi_{c1,2}$ states are reconstructed via their decay to a $rm{J}/psi$ meson, subsequently decaying into a pair of oppositely charged muons, and a photon, which is reconstructed in the calorimeter or via its conversion in the detector material. The cross-section ratio is consistent with unity in the two considered rapidity regions. Comparison with a corresponding cross-section ratio previously measured by the LHCb collaboration in $pp$ collisions suggests that $chi_{c1}$ and $chi_{c2}$ states are similarly affected by nuclear effects occurring in $p$Pb collisions.
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