  The Chern-Simons theories on a noncommutative plane, which is shown to be
describing the quantum Hall liquid, is considered. We introduce matter fields
fundamentally coupled to the noncommutative Chern-Simons field. Exploiting BPS
equations for the nonrelativistic Chern-Simons theory, we find the exact
solutions of multi vortices that are closely packed and exponentially
localized. We determine the position, the size and the angular momentum
explicitly. We then construct the solutions of two spatially separated vortices
and determine the moduli dependence of the size and the angular momentum. We
also consider the relativistic Chern-Simons theory and find nontopological
solutions whose properties are similar to the nonrelativistic counterpart.
However, unlike the nonrelativistic case, there are two branches of solutions
for a given magnetic field and they cease to exist below certain
noncommutativity scale.
