  We apply the coadjoint orbit method to construct relativistic nonlinear sigma
models (NLSM) on the target space of coadjoint orbits coupled with the
Chern-Simons (CS) gauge field and study self-dual solitons. When the target
space is given by Hermitian symmetric space (HSS), we find that the system
admits self-dual solitons whose energy is Bogomol'nyi bounded from below by a
topological charge. The Bogomol'nyi potential on the Hermitian symmetric space
is obtained in the case when the maximal torus subgroup is gauged, and the
self-dual equation in the $CP(N-1)$ case is explored. We also discuss the
self-dual solitons in the non-compact $SU(1,1)$ case and present a detailed
analysis for the rotationally symmetric solutions.
