Where the translational symmetry of a long polymer chain is interrupted, characteristic vibrations of the molecule are possible in which only those atoms at or relatively near the defect site partake of the motion. This contrasts with the more common vibrational states in which the motion propagates along the chain as a sound wave. Examples of readily producible local defects include broken bonds, missing atoms or groups, and extra links as are found, e.g., in thymine dimers. For each different defect, the spectrum of local mode frequencies is characteristic of its structure. Hence the local modes give direct information about the nature of the defect and can serve as a diagnostic signature of the polymer chain lesion. We have developed and are using algorithms and fortran code to predict the existence and nature of local modes based on their atomic structures. We have studied examples of different defects and found their eigen-frequencies and eigenvectors. For the simplest case of a broken hydrogen bond in a single A-T unit in a long homopolymer dA.dT chain, we display stereo views of the vibrating unit side-by-side with the undisturbed molecule for the three local modes occurring below 300 cm-1 in frequency.