  We construct the first binary black hole solutions of Einstein-Maxwell theory
in asymptotically anti-de Sitter space. The attractive force between the two
black holes is balanced by the addition of a background electric field, sourced
at the conformal boundary. There is a continuous family of bulk solutions for a
given boundary profile and temperature, suggesting there is continuous
non-uniqueness. We investigate the charges of the solutions and verify
numerically that they satisfy a first law of black hole mechanics relation.
