  According to a recent conjecture, the moduli space of the heterotic conformal
field theory on a $G\subset$ ADE singularity of an ALE space is equivalent to
the moduli space of a pure $\cx N=4$ supersymmetric three-dimensional gauge
theory with gauge group G. We establish this relation using geometric
engineering of heterotic strings and generalize it to theories with non-trivial
matter content. A similar equivalence is found between the moduli of heterotic
CFT on isolated Calabi--Yau 3-fold singularities and two-dimensional
Kazama-Suzuki coset theories.
