Manifestly covariant action for symmetric nonAbelian Chern-Simons theory

We study a three dimensional symmetric nonAbelian Chern-Simons theory with a general covariance and it turns out that the original Chern-Simons theory is just a gauge fixed action of the symmetric Chern-Simons theory whose constraint algebra belongs to fully first class constraint system. Furthermore a higher dimensional generalization of the analysis is performed and a five dimensional symmetric nonAbelian Chern-Simons theory is exhibited as an explicit example by using a simple and general recipe to make a first class constraint system. Finally we shall discuss some connections with the Stükelberg mechanism and matter couplings. PACS numbers:11.10.Ef, 11.10.Kk, 11.15.-q