  Assemblies of Rydberg atoms subject to resonant dipole-dipole interactions
form Frenkel excitons. We show that van-der-Waals shifts can significantly
modify the exciton wave function, whenever atoms approach each other closely.
As a result, attractive excitons and repulsive van-der-Waals interactions can
be combined to form stable one-dimensional atom chains, akin to bound
aggregates. Here the van-der-Waals shifts ensure a stronger homogeneous
delocalisation of a single excitation over the whole chain, enabling it to bind
up to six atoms. When brought into unstable configurations, such Rydberg
aggregates allow the direct monitoring of their dissociation dynamics.
