  We investigate the linearized equations of motion in three dimensional
Born-Infeld gravity theory. Motivated by this model, we calculate the
quasinormal modes of BTZ black hole solutions of parity-even gravity theories
in three dimensions by using numerical methods. The results are classified in
three families and they are so accurate such that it allows us to propose
analytical form for the quasinormal frequencies. We find new quasinormal modes
which have been missing in the literature of the analytical studies of three
dimensional massive gravitons. These new modes do not have the known tower
structure and they are purely imaginary for any value of the angular momenta.
Considering the complete set of the quasinormal modes, we show that the BTZ
black hole solutions are unstable for any value of the parameters of the
theory. We confirm our numerical results by computing the new eigenmodes
analytically at zero angular momentum.
