  We study the dynamics of certain string configurations in a class of
fivebrane supertube backgrounds. In the decoupling limit of the fivebranes,
these solutions are known to admit an exact description in worldsheet string
theory and string propagation is integrable. For the asymptotically flat
solutions, we prove, by using analytic tools of classical Hamiltonian systems,
the non-integrability of classical string motion. This suggests that string
dynamics in circular supertube geometries exhibit a regime of chaotic
behaviour.
