We propose a non-Abelian generalization of the Clebsch parametrization for
a vector in three dimensions. The construction is based on a group-theoreti
cal reduction of the Chern-Simons form on a symmetric space. The formalism
is then used to give a canonical (symplectic) discussion of non-Abelian flu
id mechanics, analogous to the way the Abelian Clebsch parametrization allo
ws a canonical description of conventional fluid mechanics.