We describe a simple strategy for calculating the cohesive energy of certain kinds of crystal using readily available quantum chemistry techniques. The strategy involves the calculation of the electron correlation energies of a hierarchy of free clusters, and the cohesive energy E(coh) is extracted from the constant of proportionality between these correlation energies and the number of atoms in the limit of large clusters. We apply the strategy to the LiH crystal, using the MP2 and CCSD(T) schemes for the correlation energy, and show that for this material E(coh) can be obtained to an accuracy of approximately 30 meV per ion pair. Comparison with the experimental value, after correction for zero-point energy, confirms this accuracy.