We present the maximally supersymmetric three-dimensional gauged supergravities. Owing to the special properties of three dimensions --- especially the on-shell duality between vector and scalar fields, and the purely topological character of (super)gravity - they exhibit an even richer structure than the gauged supergravities in higher dimensions. The allowed gauge groups are subgroups of the global E₈₍₈₎ symmetry of ungauged N = 16 supergravity. They include the regular series SO(p,8−p) × SO(p,8−p) for all p = 0,1,,4, the group E₈₍₈₎ itself, as well as various noncompact forms of the exceptional groups E₇,E₆ and F₄ × G₂. We show that all these theories admit maximally supersymmetric ground states, and determine their background isometries, which are superextensions of the anti-de Sitter group SO(2,2). The very existence of these theories is argued to point to a new supergravity beyond the standard D = 11 supergravity.