We discover a four-dimensional N=1 supersymmetric field theory that is dual to the N=4 super Yang-Mills theory with gauge group SU(2n+1) for each n. The dual theory is constructed through the diagonal gauging of the SU(2n+1) flavor symmetry of three copies of a strongly coupled superconformal field theory (SCFT) of Argyres-Douglas type. We find that this theory flows in the infrared to a strongly coupled N=1 SCFT that lies on the same conformal manifold as N=4 super Yang-Mills with gauge group SU(2n+1). Our construction provides a hint on why certain N=1, 2 SCFTs have identical central charges (a=c).