Recently we reported an unusual multilayered structure in a linear polyethylene containing precisely periodic carboxylic acid groups pendant to every 21st carbon atom (p21AA). Within the ordered domains, p21AA executes tight chain folds at the location of each acid group, and the chain fold surfaces participate in hydrogen bonds with adjacent fold surfaces to form acid-rich layers. Here, we investigate the bulk morphologies of p21AA after isothermal crystallization and, using X-ray scattering and polarized optical microscopy, find p21AA. to be semicrystalline. By analyzing X-ray peak widths, creating real-space models of lamellae, and performing in-situ X-ray scattering during tensile deformation, we find that, contrary to the typical structure of polymer crystallites, the polymer stems lie in the plane of the lamellae such that the acid layers are transverse (within 30 degrees of orthogonal) to the crystallite plane. This surprising structure, not reported before to our knowledge, could be useful for designing semicrystalline membranes because, given the appropriate chemistry, layers of functional groups could provide pathways for small molecule, ion, or proton transport through crystallites. We expect this novel structure to be accessible in similarly designed crystallizable polymers that contain evenly spaced, moderately sized, associating side groups.