We study the Chem-Simons CP(N) models with a global U(1) symmetry and
found the self-dual models among them. The Bogomolnyi-type bound in th
ese self-dual models is a nontrivial generalization of that in the pur
e CP(N) models. Our models have quite a rich vacuum and soliton struct
ure and approach the many known gauged self-dual models in an appropri
ate limit.