We consider the four-point correlator of the stress tensor multiplet in N = 4 SYM in the limit of large c=N^2, but finite \lambda=g^2 N. For finite values of \lambda single-trace intermediate operators arise at order 1/c and this leads to specific poles in the Mellin representation of the correlator. The sign of the residue at these poles is fixed by unitarity. We consider solutions consistent with crossing symmetry and this pole structure. We show that in a certain regime all solutions result in a negative contribution to the anomalous dimension of twist four operators. This positivity condition can also be proven by assuming the correct Regge behaviour for the Mellin amplitude. The positivity constraints arising from CFT for the Mellin amplitude take a very similar form to the causality constraint for the forward limit of the S-matrix.