The production of a novel two-dimensional bimolecular surface structure using weak noncovalent interactions is demonstrated and observed by scanning tunneling microscopy. This work follows the three-dimensional (3D) ideas of crystal engineering and applies the concepts of supramolecular synthons to molecular systems constrained to 2D by physisorption on a conducting surface. We demonstrate a well-ordered planar structure that self-assembles through the influence of fluorine-phenyl interactions. This study provides a concrete example of the "bottom up" construction of nanostructures and of the systematic design of self-organized layers. To our knowledge, this is the first in a new class of fully 2D materials based both upon weak intermolecular interactions and upon image charges and weak interactions associated with adsorption on metal surfaces.