  We consider the bosonic sector of a N=2 supersymmetric Chern-Simons-Higgs
theory in 2+1 dimensions. The gauge group is U(1)xU(N) and has N_f flavors of
fundamental matter fields. The model supports non-Abelian (axially symmetric)
vortices when N_f\geq N, which have internal (orientational) moduli. When N_f >
N, the solutions acquire additional collective coordinates parameterizing their
transverse size. We solve the BPS equations numerically and obtain local (N_f =
N) and semi-local (N_f > N) string solutions.
