X-ray grating interferometry is a powerful emerging tool in biomedical imaging, providing access to three complementary image modalities. In addition to the conventional attenuation modality, interferometry provides a phase modality, which visualizes soft tissue structures, and a dark-field modality, which relates to the number and size of sub-resolution scattering objects. A particularly strong dark-field signal originates from the alveoli or air sacs in the lung. Dark-field lung radiographs in animal models have already shown increased sensitivity in diagnosing lung diseases, such as lung cancer or emphysema, compared to conventional X-ray chest radiography. However, to date, X-ray dark-field lung imaging has either averaged information over several breaths or has been captured during a breath hold. In this paper, we demonstrate the first time-resolved dark-field imaging of a breath cycle in a mechanically ventilated mouse, in vivo, which was obtained using a grating interferometer. We achieved a time resolution of 0.1 s, visualizing the changes in the dark-field, phase, and attenuation images during inhalation and exhalation. These measurements show that the dark-field signal depends on the air volume and, hence, the alveolar dimensions of the lung. Conducting this type of scan with animal disease models would help to locate the optimum breath point for single-image diagnostic dark-field imaging and could indicate if the changes in the dark-field signal during breath provide a diagnostically useful complementary measure.