The dynamics of As2P2S8 quasi-molecular units caged in an As-S network in the supercooled chalcogenide liquid of composition (As2S3)(90)(P2S5)(10) have been studied near the glass transition region (T-g = 468 <= T <= 628 K) using P-31 NMR line shape analysis and spin-lattice relaxation techniques. P-31 NMR line shape analysis indicates the presence of isotropic rotational reorientation of As2P2S8 quasi-molecular units at frequencies on the order of tens of kilohertz at T < 540 K. At higher temperatures, the time scale of intramolecular bond-breaking and rearrangement is coupled to that of shear/structural relaxation of the surrounding network. On the other hand, over the entire temperature range, the P-31 NMR spin-lattice relaxation results from fast cage-rattling dynamics of the same molecules at frequencies in the megahertz to gigahertz range. When taken together, these results imply the presence of serial hierarchical dynamics in which the fast rattling of As2P2S8 quasi-molecular units trapped in their cages coexists with slower isotropic rotational reorientation. The shear or alpha-relaxation involves cooperative rearrangement of the surrounding As-S network and, consequently, relaxation of the cages that provides feedback to the fast rattling dynamics over the entire temperature range.