A general implementation of the coupled-cluster (CC) single, double, triple, and quadruple excitation (CCSDTQ) method is presented and applied to several molecules, including BH, HF, H2O, and CO with DZP basis sets. Comparisons with full CI show average errors to be 14-mu-hartree at equilibrium and 26-mu-hartree at twice R(e). CCSDTQ is exact for four electrons and is the first CC method correct through sixth order in perturbation theory.