It was recently shown that the theory obtained by deforming a general two dimensional conformal theory by the irrelevant operator $T\bar T$ is solvable. In the context of holography, a large class of such theories can be obtained by studying string theory on $AdS_3$. We show that a certain $T\bar T$ deformation of the boundary $CFT_2$ gives rise in the bulk to string theory in a background that interpolates between $AdS_3$ in the IR and a linear dilaton spacetime in the UV, i.e. to a two dimensional vacuum of Little String Theory. This construction provides holographic duals for a large class of vacua of string theory in asymptotically linear dilaton spacetimes, and sheds light on the UV behavior of $T\bar T$ deformed $CFT_2$. It may provide a step towards holography in flat spacetime.

Comment: v2: added references, v3: corrected typos and added references