Atomically smooth halogen adlayers on Ag(111) (AgX, where X = 1, Br, Cl, and F) have been prepared by quenching of heated Ag samples in concentrated acid halide (HX) solutions. The AgX adlayers are chemically stable in air for several hours, allowing detailed characterization of the adlayer atomic structures by scanning tunneling microscopy (STM). STM images of I adlayers are consistent with a nearly perfect square-root 3 x square-root 3/R30 structure; F, Cl, and Br adlayers, however, are characterized by a parallel double row structure of adsorbed halogen atoms, oriented along the [110] direction on the Ag(111) substrate. The row structure observed by STM for Cl and Br adlayers is shown to be consistent with low-energy electron diffraction (LEED) patterns, but inconsistent with the corresponding structures derived from LEED. The degree of symmetry in the various adlayers decreases with increasing adatom electronegativity, indicating that the local charge distribution around the adlayer atom and its size are the controlling factors in determining the adlayer structure.