  The recent numerical results of Dubeibe et al. [arXiv:1812.08663] were
interpreted as hinting at the existence of a fourth constant of motion
(Carter's constant) for geodesics on Chazy-Curzon spacetimes. Here we show
that, to the contrary, the geodesic dynamics of the single-particle
Chazy-Curzon spacetime exhibit features of a non-integrable system: chaotic
orbits in the meridian plane, and Birkhoff chains in the surface of section.
Thus, one should not expect Liouville-integrability, nor a fourth constant, for
this system.
