  In this paper we construct noncommutative resolutions of a certain class of
Calabi-Yau threefolds studied by F. Cachazo, S. Katz and C. Vafa. The
threefolds under consideration are fibered over a complex plane with the fibers
being deformed Kleinian singularities. The construction is in terms of a
noncommutative algebra introduced by V. Ginzburg, which we call the "N=1 ADE
quiver algebra".
