It is an accepted fact that requiring the Lovelock theory to have the maximun
possible number of degree of freedom, fixes the parameters in terms of the
gravitational and the cosmological constants. In odd dimensions, the Lagrangian
is a Chern-Simons form for the (A)dS group. In even dimensions, the action has
a Born-Infeld-like form. Recently was shown that standard odd-dimensional
General Relativity can be obtained from Chern-Simons Gravity theory for a
certain Lie algebra B. Here we report on a simple model that suggests a
mechanism by which standard even-dimensional General Relativity may emerge as a
weak coupling constant limit of a Born-Infeld theory for a certain Lie
subalgebra of the algebra B. Possible extension to the case of even-dimensional
supergravity is briefly discussed
