  We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills
phase space. The theory is well defined for an arbitrary gauge group with an
invariant bilinear form, it contains only first class constraints, and the
spacetime metric has a simple form in terms of the phase space variables. With
gauge group $SO(3,C)$, the theory equals the Ashtekar formulation of gravity
with a cosmological constant. For Lorentzian signature, the theory is complex,
and we have not found any good reality conditions. In the Euclidean signature
case, everything is real. In a weak field expansion around de Sitter spacetime,
the theory is shown to give the conventional Yang-Mills theory to the lowest
order in the fields. We show that the coupling to a Higgs scalar is
straightforward, while the naive spinor coupling does not work. We have not
found any way of including spinors that gives a closed constraint algebra. For
gauge group $U(2)$, we find a static and spherically symmetric solution.
