A symmetric two-metal-centered molecule (Ru2) is singly oxidized to form a mixed-valence complex (Ru2⁺[PF6]^-) in solution. This mixed-valence complex was adsorbed onto a metal surface and characterized by ultra-high-vacuum, low-temperature scanning tunneling microscopy (STM). Ru2⁺[PF6]^- forms a striped monolayer on Au(111) at 77 K. Each Ru2⁺ cation is imaged as a pair of circular features, and the two features appear to have different contrast in STM images. This results from the extra charge localized on one of the end groups of Ru2⁺. The presence of the [PF6]^- anion next to the charged end group may also help to localize this charge, as [PF6]^- anions are observed as small features resting next to the positively charged end groups of Ru2⁺ cations. Coulomb interactions are responsible for long-range ordering of the charge distribution within the monolayer: the charge distribution of each molecule influences and is influenced by its neighboring molecules. This sensitivity to local environment opens up the possibility of using mixed-valence molecules as memory or computing units in the molecularly based electronic devices.