  We study the two-dimensional chiral algebra associated with the simplest
Argyres-Douglas type theory with an exactly marginal coupling, i.e., the
$(A_3,A_3)$ theory. Near a cusp in the space of the exactly marginal
deformations (i.e., the conformal manifold), the theory is well-described by
the $SU(2)$ gauge theory coupled to isolated Argyres-Douglas theories and a
fundamental hypermultiplet. In this sense, the $(A_3,A_3)$ theory is an
Argyres-Douglas version of the $\mathcal{N}=2$ $SU(2)$ conformal QCD. By
studying its Higgs branch and Schur index, we identify the minimal possible set
of chiral algebra generators for the $(A_3,A_3)$ theory, and show that there is
a unique set of closed OPEs among these generators. The resulting OPEs are
consistent with the Schur index, Higgs branch chiral ring relations, and the
BRST cohomology conjecture. We then show that the automorphism group of the
chiral algebra we constructed contains a discrete group $G$ with an $S_3$
subgroup and a homomorphism $G\to S_4 \times {\bf Z}_2$. This result is
consistent with the S-duality of the $(A_3,A_3)$ theory.
