  We construct an n-dimensional Born-Infeld type gravity theory that has the
same properties as Einstein's gravity in terms of the vacuum and particle
content: Namely, the theory has a unique viable vacuum (maximally symmetric
solution) and a single massless unitary spin-2 graviton about this vacuum. The
BI gravity, in some sense, is the most natural, minimal generalization of
Einstein's gravity with a better UV behavior, and hence, is a potentially
viable proposal for low energy quantum gravity. The Gauss-Bonnet combination
plays a non-trivial role in the construction of the theory. As an extreme
example, we consider the infinite dimensional limit where an interesting
exponential gravity arises.
