Non-Abelian vortices of an 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 self interaction strength v, resulting in both attractive and repulsive phases. A detailed analysis of the properties of the solutions reveals the existence of a number of unexpected features. For a certain range of the parameter v, it is shown that the non-Abelian vortices have lower energy than their topologically stable Abelian counterparts The angular momentum of these vortices is analyzed 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.