  A sharp version of the information paradox involves a seeming violation of
the monogamy of entanglement during black hole evaporation. We construct an
analogous paradox in empty anti-de Sitter space. In a local quantum field
theory, Bell correlations between operators localized in mutually spacelike
regions are monogamous. We show, through a controlled calculation, that this
property can be violated by an order-1 factor in a theory of gravity. This
example demonstrates that what appears to be a violation of the monogamy of
entanglement may just be a subtle violation of locality in quantum gravity.
