  We consider 3-dimensional toric Calabi-Yau singularities which arise as cones
over the Chow quotient for a torus acting on projective space. We show that the
Chow forms of the closures of the codimension 2 orbits can very easily be
written down from the quiver with superpotential which corresponds with the
given CY3 singularity under the correspondence between CY3 singularities and
quivers with superpotential which is part of the AdS/CFT correspondence in
physics. We also prove that this provides a new method for computing the
principal A-determinant in the theory of Gelfand-Kapranov-Zelevinsky.
