  Using a first order Chern-Simons-like formulation of gravity we
systematically construct higher-derivative extensions of general relativity in
three dimensions. The construction ensures that the resulting higher-derivative
gravity theories are free of scalar ghosts. We canonically analyze these
theories and construct the gauge generators and the boundary central charges.
The models we construct are all consistent with a holographic c-theorem which,
however, does not imply that they are unitary. We find that Born-Infeld gravity
in three dimensions is contained within these models as a subclass.
