We show how high-resolution NMR spectra can be obtained for solids for which the spectra are normally broadened due to structural disorder. The method relies on correlations in the chemical shifts between pairs of coupled spins. It is found experimentally that there are strong correlations in the chemical shifts between neighboring spins in both phosphorus-31 and carbon-13 spectra. These correlations can be exploited not only to provide resolution in two-dimensional spectra, but also to yield "chains" of correlated chemical shifts, constituting a valuable new source of structural information for disordered materials.