  Non Abelian vortices of a SU(2) Chern-Simons--Higgs theory in 2+1 dimensions
are constructed numerically. They represent natural counterparts of the U(1)
solutions considered by Hong, Kim and Pac, and, by Jackiw and Weinberg. The
Abelian embeddings are identified, for all values of the Higgs selfinteraction
strength $\nu$, resulting in both attractive and repulsive phases. A detailed
analysis of the properties of the solutions reveals the existence ofa number of
unexpected features. For a certain range of the parameter $\nu$, it is shown
that the non Abelian vortices have lower energy than their topologically stable
Abelian counterparts, resulting in an effective energy lower bound on the SU(2)
configurations. The angular momentum of these vortices is analysed and it is
found that unlike the Abelian ones, whose angular momentum and energy are
unrelated, there is a nontrivial mass--spin relation of the non Abelian
vortices.
