Medical imaging is performed in daily clinical routine for the assessment of pulmonary involvement in patients infected with COVID-19. As conventional (attenuation-based) chest radiography provides only a low sensitivity for COVID-19-pneumonia, CT is the gold standard for lung imaging in COVID-19 patients. However, CT imaging exposes the patient to a considerable amount of radiation, and is not as widely available as plain chest X-rays. Therefore, alternative low-dose imaging X-ray techniques are highly desirable. Here we present the first clinical results employing a novel dark-field chest X-ray imaging method for the assessment of COVID-19-pneumonia. The work is based on recent technological advancements in a human-scale X-ray dark-field chest imaging prototype that enable the acquisition of quantitative dark-field radiographs with diagnostic image quality at a radiation dose comparable to conventional X-rays. In a reader study, we found that dark-field imaging has a higher sensitivity for COVID-19-pneumonia than attenuation-based imaging, and that the combination of both is superior to one imaging modality alone. Furthermore, a quantitative image analysis showed a significant reduction of signal in X-ray dark-field chest radiographs of COVID-19 patients. While our results demonstrate that dark-field chest radiography presents an ultra-low-dose alternative to CT imaging for the assessment of COVID-19-pneumonia, we anticipate that the presented technique will also be useful for therapy follow-up of patients with long-COVID-syndrome and, more generally, for the imaging of other pulmonary pathologies.