  We find a four-dimensional N=1 gauge theory which flows to the minimal
interacting N=2 superconformal field theory, the Argyres-Douglas theory, in the
infrared up to the extra free chiral multiplets. The gauge theory is obtained
from a certain N=1 preserving deformation of the N=2 SU(2) gauge theory with
four fundamental hypermultiplets. From this description, we compute the full
superconformal index and find agreements with the known results in special
limits.
