Conformational memory is introduced as a new aspect of structural relaxation of polymers. In poly(n-alkylmethacrylates) extended backbone chain conformations are identified by advanced NMR techniques as the molecular units involved in structural relaxation. They retain conformational memory over many steps of restricted axial chain motion. Randomization of conformation and isotropization of backbone orientation occur on the same time scale, yet much slower than the slowest relaxation process identified so far. Behavior typical of fragile glass formers is found for this new process of chain relaxation.