  We present a pure Chern-Simons formulation of families of interesting
Conformal Field Theories describing edge states of non-Abelian Quantum Hall
states. These theories contain two Abelian Chern-Simons fields describing the
electromagnetically charged and neutral sectors of these models, respectively.
The charged sector is the usual Abelian Chern-Simons theory that successfully
describes Laughlin-type incompressible fluids. The neutral sector is a
2+1-dimensional theory analogous to the 1+1-dimensional orbifold conformal
field theories. It is based on the gauge group O(2) which contains a ${\bf
Z}_2$ disconnected group manifold, which is the salient feature of this theory.
At level q, the Abelian theory of the neutral sector gives rise to a ${\bf
Z}_{2q}$ symmetry, which is further reduced by imposing the ${\bf Z}_2$
symmetry of charge-conjugation invariance. The remaining ${\bf Z}_q$ symmetry
of the neutral sector is the origin of the non-Abelian statistics of the
(fermionic) q-Pfaffian states.
