  We study quantum vortex states consisting of a ring of vortices with
alternating sign, in a homogeneous superfluid confined to a circular domain. We
find an exact stationary solution of the point vortex model for the neutral
vortex necklace. We investigate the stability of the necklace state within both
the point-vortex model and the Gross-Pitaevskii equation describing a trapped
atomic Bose-Einstein condensate at low temperature. The point-vortex stationary
states are found to also be stationary states of the Gross-Pitaevskii equation
provided the finite thickness of the outer fluid boundary is accounted for.
Under significant perturbation, the Gross-Pitaevskii evolution and point-vortex
model exhibit instability as expected for metastable states. The perturbed
vortex necklace exhibits sensitivity to the perturbation, suggesting a route to
seeding vortex chaos or quantum turbulence.
