  The requirements of N=1 superconformal invariance for the correlation
functions of chiral superfields are analysed. Complete expressions are found
for the three point function for the general spin case and for the four point
function for scalar superfields for \sum q_i=3 where q_i is the scale dimension
for the i'th superfield and is related to the U(1) R-charge. In the latter case
the relevant Ward identities reduce to eight differential equations for four
functions of u,v which are invariants when the superconformal symmetry is
reduced to the usual conformal group. The differential equations have a general
solution given by four linearly independent expressions involving a two
variable generalisation of the hypergeometric function. By considering the
behaviour under permutations, or crossing symmetry, the chiral four point
function is shown to be determined up to a single overall constant. The results
are in accord with the supersymmetric operator product expansion.
