Atomically smooth hexagonal boron nitride (h-BN) layers have very useful properties and thus potential applications for protective coatings, deep ultraviolet (DUV) emitters, and as a dielectric for nanoelectronics devices. In this paper, we report on the growth of h-BN by a low-pressure chemical vapor deposition (LPCVD) process using diborane and ammonia as the gas precursors. The use of LPCVD allows synthesis of h-BN with a controlled number of layers defined by the growth conditions, temperature, time, and gas partial pressure. Furthermore, few-layer h-BN was also grown by a sequential growth method, and insights into the growth mechanism are described, thus forming the basis of future growth of h-BN by atomic layer epitaxy.