Eleven-dimensional supergravity reveals large exceptional symmetries upon reduction, in accordance with the U-duality groups of M-theory, but their higher-dimensional geometric origin has remained a mystery. In this letter, we show that D = 11 supergravity can be extended to be fully covariant under the exceptional groups E n(n), n = 6, 7, 8. Motivated by a similar formulation of double field t...