Critical dimensions for chiral bosons.

We give the Lagrangian formulation of a Bose model in 1+1 dimensions which describes a free chiral Lie-algebra-valued current. This model is a non-Abelian generalization of the chiral scalar model of Siegel. Both the Abelian and non-Abelian actions have a gauge invariance, which becomes anomalous when the models are quantized. The condition that this anomaly be canceled coincides with the string no-ghost condition.