Yes, there are capillaries in the heart. The heart muscle, like any other tissue in the body, requires a constant supply of oxygen and nutrients to function properly. Capillaries are the smallest blood vessels in the body and they form a network that supplies oxygen and nutrients to the cells and removes waste products. In the heart, capillaries are found in the myocardium, the muscular layer of the heart. The coronary arteries supply blood to the capillaries in the myocardium, and the coronary veins drain blood from the capillaries.