  Non-linear special relativity (or doubly special relativity) is a simple
framework for encoding properties of flat quantum space-time. In this paper we
show how this formalism may be generalized to incorporate curvature (leading to
what might be called ``doubly general relativity''). We first propose a dual to
non-linear realizations of relativity in momentum space, and show that for such
a dual the space-time invariant is an energy-dependent metric. This leads to an
energy-dependent connection and curvature, and a simple modification to
Einstein's equations. We then examine solutions to these equations. We find the
counterpart to the cosmological metric, and show how cosmologies based upon our
theory of gravity may solve the ``horizon problem''. We discuss the
Schwarzchild solution, examining the conditions for which the horizon is energy
dependent. We finally find the weak field limit.
