  In the course of our work on low-volume hyperbolic 3-manifolds, we came upon
a linking problem for horoball necklaces in $\mathbb{H}^3$. A horoball necklace
is a collection of sequentially tangent beards (i.e. spheres) with disjoint
interiors lying on a flat table (i.e. a plane) such that each bead is of
diameter at most one and is tangent to the table. In this note, we analyze the
possible configurations of an 8-bead necklace linking around two other
diameter-one spheres on the table. We show that all the beads are forced to
have diameter one, the two linked spheres are tangent, and that each bead must
kiss (i.e. be tangent to) at least one of the two linked spheres. In fact,
there is a 1-parameter family of distinct configurations.
