A novel molecular structure prediction method, the Z Method, is described. It provides a versatile platform for the development and use of systematic, grid-based conformational search protocols, in which statistical information (i.e., rotamers) can also be included. The Z Method generates trial structures by applying many changes of the same type to a single starting structure, thereby sampling the conformation space in an unbiased way. The method, implemented in the CHARMM program as the Z Module, is applied here to an illustrative model problem in which rigid, systematic searches are performed in a 36-dimensional conformational space that describes the relative positions of the ten secondary structural elements of the protein CheY. A polar hydrogen representation with an implicit solvation term (EEF1) is used to evaluate successively larger fragments of the protein generated in a hierarchical build-up procedure. After a final refinement stage, and a total computational time of about two-and-a-half days on AMD Opteron processors, the prediction is within 1.56 Å of the native structure. The errors in the predicted backbone dihedral angles are found to approximately cancel. Monte Carlo and simulated annealing trials on the same or smaller versions of the problem, using the same atomic model and energy terms, are shown to result in less accurate predictions. Although the problem solved here is a limited one, the findings illustrate the utility of systematic searches with atom-based models for macromolecular structure prediction and the importance of unbiased sampling in structure prediction methods.