  We show that the recently proposed DBI extension of new massive gravity
emerges naturally as a counterterm in AdS$_4$. The resulting on-shell Euclidean
action is independent of the cut-off at zero temperature. We also find that the
same choice of counterterm gives the usual area law for the AdS$_4$
Schwarzschild black hole entropy in a cut-off independent manner. The parameter
values of the resulting counterterm action correspond to a $c=0$ theory in the
context of AdS$_3$/CFT$_2$. We rewrite this theory in terms of the gauge field
that is used to recast 3D gravity as a Chern-Simons theory.
