In 2017, it is hoped that the Event Horizon Telescope will generate high-resolution images of the environment around Sagittarius A*, the supermassive black hole at the centre of our galaxy. These images will allow us to observe detailed features of the black hole, including its ‘shadow’. Moreover, the outstanding detections by the Advanced LIGO collaboration have confirmed the existence of binary black hole systems. In this talk, I will analyse the shadow of a pair of black holes, using a Majumdar--Papapetrou model of two extremally charged black holes in static equilibrium. I will demonstrate that such spacetimes are natural exemplars of chaotic scattering in Hamiltonian dynamics. To describe the planar null geodesics in this spacetime, I will develop an appropriate symbolic dynamics, and demonstrate that one-dimensional binary black hole shadows can be constructed using an iterative process akin to the construction of the Cantor set. In the case of non-planar null rays, I will present three different types of one-dimensional shadow: regular; Cantor-like; and highly chaotic. We will observe that the latter are associated with the existence of stable bounded photon orbits around the two black holes.