  A generalization of the Chern-Simons-CP(1) model is considered by introducing
a nonstandard kinetic term. For a particular case, of this nonstandard kinetic
term, we show that the model support self-dual Bogomolnyi equations. The BPS
energy has a bound proportional to the sum of the magnetic flux and the CP(1)
topological charge. The self-dual equations are solved analytically and
verified numerically.
