  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 theory we introduce an extended `exceptional spacetime'. We
illustrate the construction by giving the explicit E_{6(6)} covariant form: the
full D=11 supergravity, in a 5+6 splitting of coordinates but without
truncation, embeds into an E_{6(6)} covariant 5+27 dimensional theory. We argue
that this covariant form likewise comprises type IIB supergravity.
