The release of ChatGPT, a language model capable of generating text that appears human-like and authentic, has gained significant attention beyond the research community. We expect that the convincing performance of ChatGPT incentivizes users to apply it to a variety of downstream tasks, including prompting the model to simplify their own medical reports. To investigate this phenomenon, we conducted an exploratory case study. In a questionnaire, we asked 15 radiologists to assess the quality of radiology reports simplified by ChatGPT. Most radiologists agreed that the simplified reports were factually correct, complete, and not potentially harmful to the patient. Nevertheless, instances of incorrect statements, missed key medical findings, and potentially harmful passages were reported. While further studies are needed, the initial insights of this study indicate a great potential in using large language models like ChatGPT to improve patient-centered care in radiology and other medical domains.