Room-temperature adsorption of molecular iodine on Ag(100) has been studied by scanning tunneling microscopy (STM), low-energy electron diffraction, Auger electron spectroscopy with factor analysis, and density-functional theory (DFT). We have found that at chemisorption stage iodine forms only one ordered phase described by a simple unit cell. DFT calculations have shown that energetically most favorable configuration of this square lattice corresponds to iodine atoms adsorbed in fourfold hollow sites on the silver surface. Further iodine dosing leads to the growth of two-dimensional islands of silver iodide. The STM images of the silver-iodide surface demonstrate a clear visible superstructure with a periodicity superimposed with a quasihexagonal atomic modulation. As a result of the DFT simulations of the AgI islands, a new sandwichlike phase was obtained, which appears to be different from all known bulk structures of silver iodide. In the direction perpendicular to the sample face, it consists of two coupled silver planes located between two iodine planes. According to calculations, the “sandwich,” as a whole, is situated on top of the iodine monolayer. The validity of the proposed structural model is confirmed by the excellent correspondence between experimental and simulated STM images.