Final answer:
The left coronary artery, which branches from the ascending aorta, lies in the coronary sulcus and supplies oxygenated blood to both the left ventricle and the left atrium.
Step-by-step explanation:
The blood vessel that lies in the coronary sulcus and supplies oxygenated blood to the walls of the left ventricle and the left atrium is the coronary artery, specifically, the left coronary artery. This artery arises from the ascending aorta, which is the first portion of the aorta after it arises from the left ventricle. The left coronary artery has branches such as the circumflex artery, which follows the coronary sulcus, and the anterior interventricular artery, also known as the left anterior descending (LAD) artery, which runs along the anterior interventricular sulcus.