Tin telluride (SnTe) is an IV-VI semiconductor with a topological crystalline insulator band structure, high thermoelectric performance, and in-plane ferroelectricity. Despite its many applications, there has been little work focused on understanding the growth mechanisms of SnTe thin films. In this manuscript, we investigate the molecular beam epitaxy synthesis of SnTe (111) thin films on InP (111)A substrates. We explore the effect of substrate temperature, Te/Sn flux ratio, and growth rate on the film quality. Using a substrate temperature of 340 °C, a Te/Sn flux ratio of 3, and a growth rate of 0.48 Å/s, fully coalesced and single crystalline SnTe (111) epitaxial layers with X-ray rocking curve full-width-at-half-maxima of 0.09° and root-mean-square surface roughness as low as 0.2 nm have been obtained. Despite the 7.5% lattice mismatch between the SnTe (111) film and the InP (111)A substrate, reciprocal space mapping indicates that the 15 nm SnTe layer is fully relaxed. We show that a periodic interfacial misfit (IMF) dislocation array forms at the SnTe/InP heterointerface, where each IMF dislocation is separated by 14 InP lattice sites/13 SnTe lattice sites, providing rapid strain relaxation and yielding the high quality SnTe layer. This is the first report of an IMF array forming in a rock-salt on zinc-blende material system and at an IV-VI on III-V heterointerface, and highlights the potential for SnTe as a buffer layer for epitaxial telluride film growth. This work represents an important milestone in enabling the heterointegration between IV-VI and III-V semiconductors to create multifunctional devices.