Summary: We consider scattering and capture of circular cosmic strings by a Schwarzschild black hole. Although it is a priori a very simple axially symmetric two-body problem, it shows all the features of chaotic scattering. In particular, it contains a fractal set of unstable periodic solutions; a so-called strange repellor. We study the different types of trajectories and obtain the fractal dimension of the basin boundary separating the space of initial conditions according to the different asymptotic outcomes. We also consider the fractal dimension as a function of energy, and discuss the transition from order to chaos.