  This paper presents a new formula which is conjectured to yield all tree
amplitudes in N=8 supergravity. The amplitudes are described in terms of higher
degree rational maps to twistor space. The resulting expression has manifest
N=8 supersymmetry and is manifestly permutation symmetric in all external
states. It depends monomially on the infinity twistor that explicitly breaks
conformal symmetry to Poincare. The formula has been explicitly checked to
yield the correct amplitudes for the 3-point MHV-bar and for the n-point MHV,
where it reduces to an expression of Hodges. We have also carried out numerical
checks of the formula at NMHV and NNMHV level, for up to eight external states.
