  We compute two-point functions of chiral operators Tr \Phi^3 in {\cal N}=4
SU(N) supersymmetric Yang-Mills theory to the order g^4 in perturbation theory.
We perform explicit calculations using {\cal N}=1 superspace techniques and
find that perturbative corrections to the correlators vanish for all N. While
at order g^2 the cancellations can be ascribed to the nonrenormalization
theorem valid for correlators of operators in the same multiplet as the stress
tensor, at order g^4 this argument no longer applies and the actual
cancellation occurs in a highly nontrivial way. Our result is obtained in
complete generality, without the need of additional conjectures or assumptions.
It gives further support to the belief that such correlators are not
renormalized to all orders in g and to all orders in N.
