We investigate SU(3)-periodic vortices in the self-dual Chern-Simons theory proposed by Dunne in [13, 15]. At the first admissible non-zero energy level E = 2 pi, and for each (broken and unbroken) vacuum state phi((0)) of the system, we find a family of periodic vortices asymptotically gauge equivalent to phi((0)), as the Chern-Simons coupling parameter k -> 0. At higher energy levels, we show the existence of multiple gauge distinct periodic vortices with at least one of them asymptotically gauge equivalent to the (broken) principal embedding vacuum, when k -> 0.
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