  In this note we construct a dual formulation of gravity where the main
dynamical object is affine connection. We start with the well known first order
Palatini formulation but in (Anti) de Sitter space instead of flat Minkowski
space as a background. The final result obtained by solving equations for the
metric is the Lagrangian written by Eddington in his book in 1924. Also there
is an interesting connection with attempts to construct gravitational analog of
Born-Infeld electrodynamics.
