It is the first branch of the aortic arch, and soon after it is emerges, the brachiocephalic artery divides into the right common carotid artery and the right subclavian artery.
There is no brachiocephalic artery for the left side of the body. The left common carotid, and the left subclavian artery, come directly off the aortic arch.
There are, however, two brachiocephalic veins.