The contractor renormalization group (CORE) method, a new approach to solving Hamiltonian lattice systems, is introduced. The method combines contraction and variational techniques with the real-space renormalization group approach. It applies to lattice systems of infinite extent and is suitable for studying phase structure and critical phenomena. The CORE approximation is simple to implement and is systematically improvable. The method is illustrated using the 1+1-dimensional Ising model. ((orig.)).