Structural complexity is of fundamental interest in materials science because it often results in unique physical properties and functions. Founded on this idea, the field of solid state chemistry has a long history and continues to be highly active, with new compounds discovered daily. By contrast, the area of two-dimensional (2D) materials is young but its expansion, although rapid, is limited by a severe lack of structural diversity and complexity. Here, we report a novel 2D semiconductor with a hierarchical structure composed of covalently-linked Re6Se8 clusters. The material, a 2D structural analogue of the Chevrel phase, is prepared via mechanical exfoliation of the van der Waals solid Re6Se8Cl2. Using scanning tunneling spectroscopy, photoluminescence and ultraviolet photoelectron spectroscopy, and first principles calculations, we determine the electronic bandgap (1.58 eV), optical bandgap (indirect, 1.48 eV), and exciton binding energy (100 meV) of the material. The latter is consistent with the partially 2D nature of the exciton. Re6Se8Cl2 is the first member of a new family of 2D semiconductors whose structure is built from superatomic building blocks instead of simply atoms; such structures will expand the conceptual design space for 2D materials research.