  We show that standard Einstein gravity coupled to a free conformal field
theory (CFT) in Anti de Sitter space can undergo a Higgs phenomenon whereby the
graviton acquires a nonzero mass (and three extra polarizations). We show that
the essential ingredients of this mechanism are the discreteness of the energy
spectrum in AdS space, and unusual boundary conditions on the elementary fields
of the CFT. These boundary conditions can be interpreted as implying the
existence of a 3-d defect CFT living at the boundary of the AdS space. Our
free-field computation sheds light on the essential, model-independent features
of AdS that give rise to massive gravity.
