Since December 2019, the Coronavirus Disease (COVID-19) pandemic has caused worldwide turmoil in a short period of time, and the infection, caused by SARS-CoV-2, is spreading rapidly. AI-driven tools are used to identify Coronavirus outbreaks as well as forecast their nature of spread, where imaging techniques are widely used, such as CT scans and chest X-rays (CXRs). In this paper, motivated by the fact that X-ray imaging systems are more prevalent and cheaper than CT scan systems, a deep learning-based Convolutional Neural Network (CNN) model, which we call Truncated Inception Net, is proposed to screen COVID-19 positive CXRs from other non-COVID and/or healthy cases. To validate our proposal, six different types of datasets were employed by taking the following CXRs: COVID-19 positive, Pneumonia positive, Tuberculosis positive, and healthy cases into account. The proposed model achieved an accuracy of 99.96% (AUC of 1.0) in classifying COVID-19 positive cases from combined Pneumonia and healthy cases. Similarly, it achieved an accuracy of 99.92% (AUC of 0.99) in classifying COVID-19 positive cases from combined Pneumonia, Tuberculosis, and healthy CXRs. To the best of our knowledge, as of now, the achieved results outperform the existing AI-driven tools for screening COVID-19 using the acquired CXRs, and proves the viability of using the proposed Truncated Inception Net as a screening tool.