  It is shown that General Relativity with negative cosmological constant in
three spacetime dimensions admits a new family of boundary conditions being
labeled by a nonnegative integer $k$. Gravitational excitations are then
described by "boundary gravitons" that fulfill the equations of the $k$-th
element of the KdV hierarchy. In particular, $k=0$ corresponds to the
Brown-Henneaux boundary conditions so that excitations are described by chiral
movers. In the case of $k=1$, the boundary gravitons fulfill the KdV equation
and the asymptotic symmetry algebra turns out to be infinite-dimensional,
abelian and devoid of central extensions. The latter feature also holds for the
remaining cases that describe the hierarchy ($k>1$). Our boundary conditions
then provide a gravitational dual of two noninteracting left and right KdV
movers, and hence, boundary gravitons possess anisotropic Lifshitz scaling with
dynamical exponent $z=2k+1$. Remarkably, despite spacetimes solving the field
equations are locally AdS, they possess anisotropic scaling being induced by
the choice of boundary conditions. As an application, the entropy of a rotating
BTZ black hole is precisely recovered from a suitable generalization of the
Cardy formula that is compatible with the anisotropic scaling of the chiral KdV
movers at the boundary, in which the energy of AdS spacetime with our boundary
conditions depends on $z$ and plays the role of the central charge. The
extension of our boundary conditions to the case of higher spin gravity and its
link with different classes of integrable systems is also briefly addressed.
