  It has been recently shown that the deformation of an arbitrary
two-dimensional conformal field theory by the composite irrelevant operator $T
\bar T$, built from the components of the stress tensor, is solvable; in
particular, the finite-size spectrum of the deformed theory can be obtained
from that of the original CFT through a universal formula. We study a similarly
universal, Lorentz-breaking deformation of two-dimensional CFTs that posess a
conserved $U(1)$ current, $J$. The deformation takes the schematic form $J \bar
T$ and is interesting because it preserves an $SL(2,\mathbb{R}) \times U(1)$
subgroup of the original global conformal symmetries. For the case of a purely
(anti)chiral current, we find the finite-size spectrum of the deformed theory
and study its thermodynamic properties. We test our predictions in a simple
example involving deformed free fermions.
