This article reports the first measurement of prompt χc1 and χc2 charmonium production in nuclear collisions at Large Hadron Collider energies. The cross-section ratio σ(χc2)/σ(χc1) is measured in pPb collisions at √sNN=8.16 TeV, collected with the LHCb experiment. The χc1,2 states are reconstructed via their decay to a J/ψ 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 χc1 and χc2 states are similarly affected by nuclear effects occurring in pPb collisions.Received 17 March 2021Accepted 23 April 2021DOI:https://doi.org/10.1103/PhysRevC.103.064905Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.©2021 CERN, for the LHCb CollaborationPhysics Subject Headings (PhySH)Particle & resonance productionResearch AreasRelativistic heavy-ion collisionsParticle & resonance productionResearch AreasParticle & resonance productionRelativistic heavy-ion collisionsNuclear Physics