The structure of the chemisorbed uracil overlayer that is formed on Ag(111) at potentials positive to -0.70 V (SCE) following a two-dimensional disorder-order phase transition, has been investigated by in situ STM. The uracil molecules are arranged in parallel rows, the distance between the rows, 10.5 +/- 0.5 Angstrom, being appreciably greater than that between uracil molecules within a row, 6.5 +/- 0.2 Angstrom. A packing model in which the rows consist of chains of flat, H-bonded uracil molecules is hypothesized. The domains of regularly arranged molecules cover the electrode surface completely only at uracil bulk concentrations c > 4 x 10(-4) M. At lower c values a steady state is attained in which the surface coverage by the domains is < 1 and decreases with a decrease in c.