Sum rules for products of two, three and four quantum chromodynamics (QCD) currents are derived using chiral symmetry at infinite momentum in the large-N limit. These exact relations among meson decay constants, axial-vector couplings and masses determine the asymptotic behaviour of an infinite number of QCD correlators. The familiar spectral function sum rules for products of two QCD currents are among the relations derived. With this precise knowledge of asymptotic behaviour, an infinite number of large-N QCD correlators can be constructed using dispersion relations. A detailed derivation is given of the exact large-N pion vector form factor and forward pion-pion scattering amplitudes.