Epitaxial SnTe (111) is grown by molecular-beam epitaxy on Bi2Te3 substrates. Structural evaluation indicates that SnTe deviates from cubic due to in-plane compressive strain, which induces significant changes in the electronic band structure. More specifically, a pair of gapless crossings between the two uppermost valence bands occurs in k space along the out-of-plane ΓZ direction of the Brillouin zone, associated with a band inversion, thus defining topological three-dimensional Dirac nodes. Combined first-principles calculations and angle-resolved photoelectron spectroscopy reveal an overtilted Dirac cone indicating that the crossing is a topological type-III Dirac node at the borders between type-I and type-II Dirac nodes.