  Chiral orbifold models are defined as gauge field theories with a finite
gauge group $\Gamma$. We start with a conformal current algebra A associated
with a connected compact Lie group G and a negative definite integral invariant
bilinear form on its Lie algebra. Any finite group $\Gamma$ of inner
automorphisms or A (in particular, any finite subgroup of G) gives rise to a
gauge theory with a chiral subalgebra $A^{\Gamma}\subset A$ of local
observables invariant under $\Gamma$. A set of positive energy $A^{\Gamma}$
modules is constructed whose characters span, under some assumptions on
$\Gamma$, a finite dimensional unitary representation of $SL(2,Z)$. We compute
their asymptotic dimensions (thus singling out the nontrivial orbifold modules)
and find explicit formulae for the modular transformations and hence, for the
fusion rules.
  As an application we construct a family of rational conformal field theory
(RCFT) extensions of $W_{1+\infty}$ that appear to provide a bridge between two
approaches to the quantum Hall effect.
