  In this paper the universal enveloping algebra of color hom-Lie algebras is
studied. A construction of the free involutive hom-associative color algebra on
a hom-module is described and applied to obtain the universal enveloping
algebra of an involutive hom-Lie color algebra. Finally, the construction is
applied to obtain the well-known Poincar{\'e}-Birkhoff-Witt theorem for Lie
algebras to the enveloping algebra of an involutive color hom-Lie algebra.
