We report ab initio calculations for the unreconstructed surface electronic properties of metastable FeSi(CsCl)(111). This phase, not present in bulk, can be epitaxially grown on Si(111) and exhibits an extremely rare etal-silicon bond, with Si coordinated to eight Fe atoms. A fully self-consistent density functional theory approach using pseudopotentials and a basis set of numerical atomic orbitals was used to study the surface relaxations and electronic structure for both Fe and Si terminated surfaces. In both cases, two Shockley surface states, with major weight on Fe atoms, appear in the hybridization gap, even when Fe is not in the outermost layer. For the Si on top geometry, another mixed Shockley-Tamm surface band arises which agrees very well with angle-resolved photoemission spectroscopy experiments, strongly suggesting a Si terminated surface for this material.