Solve this by matching each candidate structure to the specific foramen that actually transmits it. The foramen magnum is the broad central aperture in the occipital bone where the brainstem and spinal cord join; its job is to let the medulla pass plus a defined set of vessels and ligaments.
The genuine contents of the foramen magnum include the medulla oblongata with its meninges, both vertebral arteries, the anterior and posterior spinal arteries, the spinal part of the accessory nerve heading upward, and the membrana tectoria together with the alar ligaments.
Now place each option in its correct opening. The internal carotid artery travels through the carotid canal of the temporal bone. The sympathetic chain runs as the cervical chain anterior to the transverse processes and does not traverse the foramen magnum. The hypoglossal nerve exits through the hypoglossal canal in the occipital bone. The vertebral artery, on the other hand, ascends through the transverse foramina and then enters the skull via the foramen magnum.
Only the vertebral artery is on the foramen magnum list, so it is the answer.
\[\boxed{\text{Vertebral artery}}\]