  The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by
$G_L\otimes G_R$. In the standard gauged WZW theory, vector gauge fields (\ie\
with vector gauge couplings) are in the adjoint representation of the subgroup
$H \subset G$. In this paper, we show that, in the conformal limit in two
dimensions, there is a gauged WZW theory where the gauge fields are chiral and
belong to the subgroups $H_L$ and $H_R$ where $H_L$ and $H_R$ can be different
groups. In the special case where $H_L=H_R$, the theory is equivalent to vector
gauged WZW theory. For general groups $H_L$ and $H_R$, an examination of the
correlation functions (or more precisely, conformal blocks) shows that the
chiral gauged WZW theory is equivalent to $(G/H)_L\otimes (G/H)_R$ coset models
in conformal field theory. The equivalence of the vector gauged WZW theory and
the corresponding $G/H$ coset theory then follows.
