The tetratricopeptide repeat (TPR) is a 34-amino acid α-helical motif that occurs in over 300 different proteins. In the different proteins, three to sixteen or more TPR motifs occur in tandem arrays and function to mediate protein-protein interactions. The binding specificity of each TPR protein is different, although the underlying structural motif is the same. Here we describe a statistical approach to the design of an idealized TPR motif. We present the high-resolution X-ray crystal structures (to 1.55 and 1.6 Å) of designed TPR proteins and describe their solution properties and stability. A detailed analysis of these structures provides an understanding of the TPR motif, how it is repeated to give helical arrays with different superhelical twists, and how a very stable framework may be constructed for future functional designs.