  In this paper we will analyse the deformation of a ABJ theory in harmonic
superspace. So, we will first discuss deformations of the harmonic superspace
by a graviphoton background and then study the ABJ theory in this deformed
harmonic superspace. This deformed ABJ theory will be shown to posses
$\mathcal{N} =6$ supersymmetry. We also discuss the BRST symmetry of this
theory.
