The (111) surface of SnTe hosts one isotropic (Gamma) over bar -centered and three degenerate anisotropic (M) over bar -centered Dirac surface states. We predict that a nematic phase with spontaneously broken C-3 symmetry will occur in the presence of a perpendicular magnetic field when the N = (M) over bar Landau levels are 1/3 or 2/3 filled. The nematic state phase boundary is controlled by a competition between intravalley Coulomb interactions that favor a valley-polarized state and weaker intervalley scattering processes that increase in relative strength with magnetic field. An in-plane Zeeman field alters the phase diagram by lifting the threefold (M) over bar Landau-level degeneracy, yielding a ground state energy with 2 pi/3 periodicity as a function of Zeeman-field orientation angle.