It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator T (T) over bar, 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 possess a conserved U (1) current, J. The deformation takes the schematic form J (T) over bar and is interesting because it preserves an SL (2, R)xU (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.