  We study D1-branes on the fourfold $\C^4/(\Z_2\times\Z_2\times\Z_2)$, in the
presence of discrete torsion. Discrete torsion is incorporated in the gauge
theory of the D1-branes by considering a projective representation of the
finite group $\Z_2\times\Z_2\times\Z_2$. The corresponding orbifold is then
deformed by perturbing the F-flatness condition of the gauge theory. The moduli
space of the resulting gauge theory retains a stable singularity of codimension
three.
