  We investigate finite energy solutions of the
Einstein--Yang-Mills--Chern-Simons system in odd spacetime dimensions, D=2n+1,
with n>1. Our configurations are static and spherically symmetric, approaching
at infinity a Minkowski spacetime background. In contrast with the Abelian
case, the contribution of the Chern-Simons term is nontrivial already in the
static, spherically symmetric limit. Both globally regular, particle-like
solutions and black holes are constructed numerically for several values of D.
These solutions carry a nonzero electric charge and have finite mass. For
globally regular solutions, the value of the electric charge is fixed by the
Chern-Simons coupling constant. The black holes can be thought as non-linear
superpositions of Reissner-Nordstrom and non-Abelian configurations. A
systematic discussion of the solutions is given for D=5, in which case the
Reissner-Nordstrom black hole becomes unstable and develops non-Abelian hair.
We show that some of these non-Abelian configurations are stable under linear,
spherically symmetric perturbations. A detailed discussion of an exact D=5
solution describing extremal black holes and solitons is also provided.
