  We exploit the power and potential of the (anti-)chiral superfield approach
(ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the nilpotent
(anti-)BRST symmetry transformations for any arbitrary D-dimensional
interacting non-Abelian 1-form gauge theory where there is a SU(N) gauge
invariant coupling between the gauge field and the Dirac fields. We derive the
conserved and nilpotent (anti-)BRST charges and establish their nilpotency and
absolute anticommutativity properties within the framework of ACSA to BRST
formalism. The clinching proof of the absolute anticommutativity property of
the conserved and nilpotent (anti-)BRST charges is a novel result in view of
the fact that we consider, in our present endeavor, only the (anti-)chiral
super expansions of the superfields that are defined on the (D, 1)-dimensional
super-submanifolds of the general (D, 2)-dimensional supermanifold on which our
D-dimensional ordinary interacting non-Abelian 1-form gauge theory is
generalized. To corroborate the novelty of the above result, we apply the ACSA
to an N = 2 supersymmetric (SUSY) quantum mechanical (QM) model of a harmonic
oscillator and show that the nilpotent and conserved N = 2 supercharges of this
system do not absolutely anticommute.
