  We consider the vortex structure of a rapidly rotating trapped atomic
Bose-Einstein condensate in the presence of a co-rotating periodic optical
lattice potential. We observe a rich variety of structural phases which reflect
the interplay of the vortex-vortex and vortex-lattice interactions. The lattice
structure is very sensitive to the ratio of vortices to pinning sites and we
observe structural phase transitions and domain formation as this ratio is
varied.
