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