  It is well known that a local, unitary Poincare-invariant 2D QFT with a
global scaling symmetry and a discrete non-negative spectrum of scaling
dimensions necessarily has both a left and a right local conformal symmetry. In
this paper we consider a chiral situation beginning with only a left global
scaling symmetry and do not assume Lorentz invariance. We find that a left
conformal symmetry is still implied, while right translations are enhanced
either to a right conformal symmetry or a left U(1) Kac-Moody symmetry.
