Personal health data is subject to privacy regulations, making it challenging to apply centralized data-driven methods in healthcare, where personalized training data is frequently used. Federated Learning (FL) promises to provide a decentralized solution to this problem. In FL, siloed data is used for the model training to ensure data privacy. In this paper, we investigate the viability of the federated approach using the detection of COVID-19 pneumonia as a use case. 1411 individual chest radiographs, sourced from the public data repository COVIDx8 are used. The dataset contains radiographs of 753 normal lung findings and 658 COVID-19 related pneumonias. We partition the data unevenly across five separate data silos in order to reflect a typical FL scenario. For the binary image classification analysis of these radiographs, we proposeResNetFed, a pre-trained ResNet50 model modified for federation so that it supportsDifferential Privacy. In addition, we provide a customized FL strategy for the model training with COVID-19 radiographs. The experimental results show that ResNetFed clearly outperforms locally trained ResNet50 models. Due to the uneven distribution of the data in the silos, we observe that the locally trained ResNet50 models perform significantly worse than ResNetFed models (mean accuracies of 63% and 82.82%, respectively). In particular, ResNetFed shows excellent model performance in underpopulated data silos, achieving up to +34.9 percentage points higher accuracy compared to local ResNet50 models. Thus, with ResNetFed, we provide a federated solution that can assist the initial COVID-19 screening in medical centers in a privacy-preserving manner.