  Recently, a non-local yet possibly UV-complete quantum field theory has been
constructed by deforming a two-dimensional CFT by the composite operator $J
\bar T$, where $J$ is a chiral $U(1)$ current and $\bar T$ is a component of
the stress tensor. Assuming the original CFT was a holographic CFT, we work out
the holographic dual of its $J \bar T$ deformation. We find that the dual
spacetime is still AdS$_3$, but with modified boundary conditions that mix the
metric and the Chern-Simons gauge field dual to the $U(1)$ current. We show
that when the coefficient of the chiral anomaly for $J$ vanishes, the energy
and thermodynamics of black holes obeying these modified boundary conditions
precisely reproduce the previously derived field theory spectrum and
thermodynamics. Our proposed holographic dictionary can also reproduce the
field-theoretical spectrum in presence of the chiral anomaly, upon a certain
assumption that we justify. The asymptotic symmetry group associated to these
boundary conditions consists of two copies of the Virasoro and one copy of the
$U(1)$ Ka\v{c}-Moody algebra, just as before the deformation; the only effect
of the latter is to modify the spacetime dependence of the right-moving
Virasoro generators, whose action becomes state-dependent and effectively
non-local.
