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There is discernable and significant band dispersion along both high symmetry directions for cleaved ordered surfaces of the layered In4Se3(001). The extent of dispersion of approximately 1 eV is observed along the surface chain rows, and about 0.5 eV perpendicular to the surface “furrows,” consistent with theoretical expectations. A possible surface state exists at the surface Brillouin zone edge, in the direction perpendicular to the chains, in a gap of the projected bulk band structure. Excluding the possible surface state, the experimental hole mass is 5.5 times greater along the chains than perpendicular to the chains, but the dispersion is easier to discern.