A novel approach for a delay line interferometer (DLI) based on transmission Bragg scattering is proposed. We have numerically and experimentally demonstrated for the first time, to the best of our knowledge, that a Bragg grating (BG) can deliver the functionality of a DLI in its transmission mode along a single common interfering optical path, instead of the conventional DLI implementation with two interfering optical paths. As a proof of concept, phase-modulated fiber BGs have been designed and fabricated, showing the desired functionality in the transmission mode of the BG. The proposed approach is applicable to any kind of BG technology, such as volume BGs, dielectric mirrors, silicon photonics, and other optical waveguide-based Bragg structures.