  I derive a procedure to count chiral primary states in N=1 superconformal
field theories in four dimensions. The chiral primaries are counted by putting
the N=1 field theory on S^3 X R. I also define an index that counts semi-short
multiplets of the superconformal theory. I construct N=1 supersymmetric
Lagrangians on S^3 X R for theories which are believed to flow to a conformal
fixed point in the IR. For ungauged theories I reduce the field theory to a
supersymmetric quantum mechanics, whereas for gauge theories I use chiral ring
arguments. I count chiral primaries for SU(2) SYM with three flavors and its
Seiberg dual. Those two results agree provided a new chiral ring relation
holds.
