We study the four point correlator of the stress-energy tensor in N=4 SYM at leading order in inverse powers of the central charge. This corresponds to the Anti-deSitter version of the Virasoro-Shapiro amplitude. At large t'Hooft coupling lambda, we use dispersive sum rules to relate the Wilson coefficients in a 1/lambda expansion to the OPE data of heavy string operators. Assuming that the Wilson coefficients are in the ring of single valued multiple zeta values (as is expected for closed string amplitudes), we solve the dispersion relations to get the first 1/R^2 correction to the flat space amplitude.