We consider the motion of chains of inertial particles interacting elastically near rotationally coherent Lagrangian vortices in quasigeostrophic flow. We find that, while cyclonic (anticyclonic) such vortices attract (repel) light (heavy) inertial particles and vice versa, sufficiently stiff elastic inertial chains are attracted by the vortices independent of the buoyancy of the chain particles and the polarity of the vortices. Our result provides a possible explanation for the observed tendency of \emph{Sargassum} mats to get collected inside mesoscale eddies in the ocean. (Support provided by CONACyT-SENER.)