We examined the effects of rhythmic expansion of alveolar walls on fluid mechanics in the pulmonary acinus. We generated a realistic geometric model of an alveolated duct that expanded and contracted in a geometrically similar fashion to simulate tidal breathing. Time-dependent volumetric flow was generated by adjusting the proximal and distal boundary conditions. The low Reynolds number velocity field was solved numerically over the physiological range. We found that for a given geometry, the ratio of the alveolar flow (QA) to the ductal flow (QD) played a major role in determining the flow pattern. For larger QA/QD (as in the distal region in the acinus), the flow in the alveolus was largely radial. For small QA/QD (as in the proximal region in the acinus), the flow in the alveolus was slowly rotating and the velocity field near the alveolar opening was complex with a stagnation saddle point typical of chaotic flow structures. Performing Lagrangian fluid particle tracking, we demonstrated that in such a flow structure the motion of fluid could be highly complex, irreversible, and unpredictable even though it was governed by simple deterministic equations. These are the characteristics of chaotic flow behavior. We conclude that because of the unique geometry of alveolated duct and its time-dependent motion associated with tidal breathing, chaotic flow and chaotic mixing can occur in the lung periphery. Based on these novel observations, we suggest a new approach for studying acinar fluid mechanics and aerosol kinetics.