Chronic Obstructive Pulmonary Disease (COPD) is a leading cause of morbidity and mortality worldwide. Identifying those at highest risk of deterioration would allow more effective distribution of preventative and surveillance resources. Secondary pulmonary hypertension is a manifestation of advanced COPD, which can be reliably diagnosed by the main Pulmonary Artery (PA) to Ascending Aorta (Ao) ratio. In effect, a PA diameter to Ao diameter ratio of greater than 1 has been demonstrated to be a reliable marker of increased pulmonary arterial pressure. Although clinically valuable and readily visualized, the manual assessment of the PA and the Ao diameters is time consuming and under-reported. The present study describes a non invasive method to measure the diameters of both the Ao and the PA from contrast-enhanced chest Computed Tomography (CT). The solution applies deep learning techniques in order to select the correct axial slice to measure, and to segment both arteries. The system achieves test Pearson correlation coefficient scores of 93% for the Ao and 92% for the PA. To the best of our knowledge, it is the first such fully automated solution.