  We explicitly compute the complete three-loop (O(g^4)) contribution to the
four-point function of chiral primary current-like operators <(q)^2 q^2 (q)^2
q^2> in any finite N=2 SYM theory. The computation uses N=2 harmonic
supergraphs in coordinate space. Dramatic simplifications are achieved by a
double insertion of the N=2 SYM linearized action, and application of
superconformal covariance arguments to the resulting nilpotent six-point
amplitude. The result involves polylogarithms up to fourth order of the
conformal cross ratios. It becomes particularly simple in the N=4 special case.
