We exploit the beauty and strength of the symmetry invariant restrictions on the (anti)chiral superfields to derive the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, and (anti-)co-BRST symmetry transformations in the case of a two $(1+1)$-dimensional (2$D$) self-dual chiral bosonic field theory within the framework of augmented (anti)chiral superfield formalism. Our 2$D$ ordinary theory is generalized onto a $\left(\mathrm{2,2}\right)$-dimensional supermanifold which is parameterized by the superspace variable $Z^M=\left(x^{\mu },\theta ,\overline{\theta }\right)$, where $x^{\mu }$ (with $\mu =\mathrm{0,1}$) are the ordinary 2$D$ bosonic coordinates and ($\theta ,\overline{\theta }$) are a pair of Grassmannian variables with their standard relationships: ${\theta }^2={\overline{\theta }}^2=0$, $\theta \overline{\theta }+\overline{\theta }\theta =0$. We impose the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti)chiral superfields (defined on the (anti)chiral $\left(\mathrm{2,1}\right)$-dimensional supersubmanifolds of the above general $\left(\mathrm{2,2}\right)$-dimensional supermanifold) to derive the above nilpotent symmetries. We do not exploit the mathematical strength of the (dual-)horizontality conditions anywhere in our present investigation. We also discuss the properties of nilpotency, absolute anticommutativity, and (anti-)BRST and (anti-)co-BRST symmetry invariance of the Lagrangian density within the framework of our augmented (anti)chiral superfield formalism. Our observation of the absolute anticommutativity property is a completely novel result in view of the fact that we have considered only the (anti)chiral superfields in our present endeavor.