  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.
