This work presents a comprehensive quantum dynamics calculation of the bound rovibrational eigenstates of argon trimer (Ar3), using the ScalIT suite of parallel codes. The Ar3 rovibrational energy levels are computed to a very high level of accuracy (10-3 cm-1 or better), and up to the highest rotational and vibrational excitations for which bound states exist. For many of these rovibrational states, wavefunctions are also computed. Rare gas clusters such as Ar3 are interesting because the interatomic interactions manifest through long-range van der Waals forces, rather than through covalent chemical bonding. As a consequence, they exhibit strong Coriolis coupling between the rotational and vibrational degrees of freedom, as well as highly delocalized states, all of which renders accurate quantum dynamical calculation difficult. Moreover, with its (comparatively) deep potential well and heavy masses, Ar3 is an especially challenging rare gas trimer case. There are a great many rovibrational eigenstates to compute, and a very high density of states. Consequently, very few previous rovibrational state calculations for Ar3 may be found in the current literature - and only for the lowest-lying rotational excitations.