Medical imaging has been used for diagnosis of various conditions, making it one of the most powerful resources for effective patient care. Due to widespread availability, low cost, and low radiation, chest X-ray is one of the most sought after radiology examination for the diagnosis of various thoracic diseases. Due to advancements in medical imaging technologies and increasing patient load, current radiology workflow faces various challenges including increasing backlogs, working long hours, and increase in diagnostic errors. An automated computer-aided diagnosis system that can interpret chest X-rays to augment radiologists by providing actionable insights has potential to provide second opinion to radiologists, highlight relevant regions in the image, in turn expediting clinical workflow, reducing diagnostic errors, and improving patient care. In this study, we applied a novel architecture augmenting the DenseNet121 Convolutional Neural Network (CNN) with multi-head self-attention mechanism using transformer, namely SA-DenseNet121, that can identify multiple thoracic diseases in chest X-rays. We conducted experiments on four of the largest chest X-ray datasets, namely, ChestX-ray14, CheXpert, MIMIC-CXR-JPG, and IU-CXR. Experimental results in terms of area under the receiver operating characteristics (AUC-ROC) shows that augmenting CNN with self-attention has potential in diagnosing different thoracic diseases from chest X-rays. The proposed methodology has the potential to support the reading workflow, improve efficiency, and reduce diagnostic errors.