In this report, we describe a process for achieving atomically smooth, few-layer thick, hexagonal boron nitride (h-BN) films on sapphire substrates by MOCVD, using Triethylboron (TEB) and NH3 as precursors. Two different growth modes have been observed depending on the V/III ratio. Three-dimensional (3D) island growth is dominant in the low V/III range; in this range growth rate decreases with increasing deposition temperature. This island growth mode transitions to a self-terminating growth mode when V/III > 2000, over the entire deposition temperature range studied (i.e. 1000-1080oC). Raman spectroscopy verifies the h-BN phase of these films, and atomic force microscopy measurements confirm that the surfaces are smooth and continuous, even over atomic steps on the surface of the substrate. Using X-ray reflectance measurements, the thickness of each film grown under a range of conditions and times was determined to consistently terminate at 1.6nm, with a variation of less than 0.2 nm. Thus we have identified a self-terminating growth mode that enables robust synthesis of h-BN with highly uniform and reliable thickness on non-metal catalyzed substrates. Furthermore, this self-terminating growth behavior has shown signs of transitioning to continuous growth as deposition temperature increases.