We investigate the application of stationary Digital Tomosynthesis (DTS) using distributed x-ray source arrays for retrospectively-gated dynamic chest imaging under free-breathing conditions. The new capability might provide improved assessment of lung function impairment. A high-fidelity polychromatic x-ray system model was used to simulate a dynamic DTS configuration consisting of a linear array of 42 sources covering a 27.2° angular range in the superior-inferior direction. The array was placed 130 cm from a 42x42 cm flat-panel detector (FPD) with 0.56 mm pixels. The object center was placed at 116 cm from the source array. Dynamic acquisitions of a deformable digital chest phantom undergoing a realistic respiratory cycle (4 sec period) were simulated. The x-ray sources in the array were sequentially rastered at 8 fps; multiple passes through the array were performed to cover 3-19 breathing cycles. For reconstruction (0.5 mm voxels) of a given respiratory phase, a short sequence of projections temporally centered on the phase of interest was extracted from each cycle. The length of this sequence was varied from 1 (exact gating) to 5 frames. We investigated tradeoffs in motion blur (worse with longer gating), sampling artifacts (better with more breathing cycles), and noise, assuming a fixed total scan dose of 20 mAs regardless of the number of source array passes. A DTS acquisition over 15 respiratory cycles with exact gating yields breathing phase reconstructions at inspiration, expiration, and mid-cycle that recover >70% of the contrast in a static reconstruction and achieve adequate suppression of undersampling artifacts. For expiration and expiration, wide gating with 3 views/cycle can be used to reduce noise and improve sampling without introducing appreciable motion blur (>65% contrast recovery). For intermediate respiratory phases, wide gating causes motion blur that may require algorithmic compensation. Dynamic lung imaging with stationary DTS is feasible with approx. 1 min scan time and retrospective gating.