The most frequent cause of Aortic Aneurysms is atherosclerosis. Major risk factors include a high level of LDL cholesterol, smoking, and diabetes. The arterial wall thins as result of destruction of the media and a localized dilatation occurs (aneurysm).
You can see the aneurysm here as a bulge in the thoracic aorta. Atherosclerosis is usually more severe distally in the aorta, perhaps because the blood flow might be more turbulent here. So most atherosclerotic aneurysms occur in the abdomen, although the pulse pressure is actually higher in the chest.
Advanced syphilis, the classic cause of thoracic aortic aneurysms, is thankfully uncommon today.