  In this paper we will discuss non-anticommutative deformations of the
harmonic superspace. We will analyse the non-anticommutative deformation of the
superspace that break the supersymmetry from $\mathcal{N} =3$ supersymmetry to
$\mathcal{N} =2$ supersymmetry. We will then study the ABJ theory in this
non-anticommutative superspace. This deformed ABJ theory will be shown to
posses $\mathcal{N} =5$ supersymmetry.
