The LHCb Collaboration measures production of the exotic hadron χ_{c1}(3872) in proton-nucleus collisions for the first time. Comparison with the charmonium state ψ(2S) suggests that the exotic χ_{c1}(3872) experiences different dynamics in the nuclear medium than conventional hadrons, and comparison with data from proton-proton collisions indicates that the presence of the nucleus may modify χ_{c1}(3872) production rates. This is the first measurement of the nuclear modification factor of an exotic hadron.