We perform the canonical quantization for a system of non-Abelian chiral bosons. We show that unlike in the Wess-Zumino-Witten model, the left- and right-handed current densities do not simultaneously span Kac-Moody algebras in the quantum theory. At the critical values of the coupling constants, only one Kac-Moody algebra results. © 1989 The American Physical Society.