  A covariant formalism for Moyal deformations of gauge theory and differential
equations which determine Seiberg-Witten maps is presented. Replacing the
ordinary product of functions by the noncommutative Moyal product,
noncommutative versions of integrable models can be constructed. We explore how
a Seiberg-Witten map acts in such a framework. As a specific example, we
consider a noncommutative extension of the principal chiral model.
