  It is shown how a chiral Wess-Zumino-Witten theory with globally defined
vertex operators and a one-to-one correspondence between fields and states can
be constructed. The Hilbert space of this theory is the direct sum of tensor
products of representations of the chiral algebra and finite dimensional
internal parameter spaces. On this enlarged space there exists a natural action
of Drinfeld's quasi quantum group $A_{g,t}$, which commutes with the action of
the chiral algebra and plays the r\^{o}le of an internal symmetry algebra. The
$R$ matrix describes the braiding of the chiral vertex operators and the
coassociator $\Phi$ gives rise to a modification of the duality property.
  For generic $q$ the quasi quantum group is isomorphic to the coassociative
quantum group $U_{q}(g)$ and thus the duality property of the chiral theory can
be restored. This construction has to be modified for the physically relevant
case of integer level. The quantum group has to be replaced by the
corresponding truncated quasi quantum group, which is not coassociative because
of the truncation. This exhibits the truncated quantum group as the internal
symmetry algebra of the chiral WZW model, which therefore has only a modified
duality property. The case of $g=su(2)$ is worked out in detail.
