Chest radiography is a relatively cheap, widely available medical procedure that conveys key information for making diagnostic decisions. Chest X-rays are frequently used in the diagnosis of respiratory diseases such as pneumonia or COVID-19. In this paper, we propose a self-supervised deep neural network that is pretrained on an unlabeled chest X-ray dataset. Pretraining is achieved through the contrastive learning approach by comparing representations of differently augmented input images. The learned representations are transferred to downstream tasks – the classification of respiratory diseases. We evaluate the proposed approach on two tasks for pneumonia classification, one for COVID-19 recognition and one for discrimination of different pneumonia types. The results show that our approach yields competitive results without requiring large amounts of labeled training data.