Cu4Mo6Se8 has been synthesized by intercalation of Cu into Cu2Mo6Se8 at room temperature, and its crystal structure has been determined. This compound crystallizes in the triclinic space group P (1) over bar, with a = 6.7609(8) angstrom, b = 6.8122(7) angstrom, c = 7.9355(10) angstrom, alpha = 70.739(4)degrees, beta = 72.669(4)degrees, gamma = 84.555(5)degrees, and Z = 1. Instead of residing in the voids between corners or edges of Mo6Se8 clusters as in the classic R (3) over bar Chevrel structure, the Cu atoms in Cu4Mo6Se8 fully occupy four sites between faces of two adjacent Mo6Se8 clusters. Thus, two of the six Mo atoms in each cluster do not have capping Se atoms from neighboring clusters. This represents a new triclinic structure type for Chevrel phases. In addition to the synthesis and crystal structure, we present and discuss results from electronic structure calculations using both extended Huckel and density functional theory. These calculations predict Cu4Mo6Se8 to be metallic. We also report results from Cu intercalation into Chevrel phase sulfides and tellurides. Preliminary experiments suggest that a telluride analogue of Cu4Mo6Se8 exists.