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We study the $T\bar{T}$ deformation of the chiral bosons and show theequivalence between the chiral bosons of opposite chiralities and the scalarfields at the Hamiltonian level under the deformation. We also derive thedeformed Lagrangian of more generic theories which contain an arbitrary numberof chiral bosons to all orders. By using these results, we derive the$T\bar{T}$ deformed boundary action of the AdS$_3$ gravity theory in theChern-Simons formulation. We compute the deformed one-loop torus partitionfunction, which satisfies the $T\bar{T}$ flow equation up to the one-looporder. Finally, we calculate the deformed stress tensor of a solutiondescribing a BTZ black hole in the boundary theory, which coincides with theboundary stress tensor derived from the BTZ black hole with a finite cutoff.

$T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS$_3$ gravity