The design and synthesis of two-dimensional (2D) polymers is a challenging task, hitherto achieved in solution only through the aid of a solid surface "template" or preorganization of the building blocks in a 2D confined space. We present a novel approach for synthesizing free-standing, covalently bonded, single-monomer-thick 2D polymers in solution without any preorganization of building blocks on solid surfaces or interfaces by employing shape-directed covalent self-assembly of rigid, disk-shaped building blocks having laterally predisposed reactive groups on their periphery. We demonstrate our strategy through a thiol-ene "click" reaction between (allyloxy)12CB, a cucurbituril (CB) derivative with 12 laterally predisposed reactive alkene groups, and 1,2-ethanedithiol to synthesize a robust and readily transferable 2D polymer. We can take advantage of the high binding affinity of fully protonated spermine (positive charges on both ends) to CB to keep each individual polymer sheet separated from one another by electrostatic repulsion during synthesis, obtaining, for the first-time ever, a single-monomer-thick 2D polymer in solution. The arrangement of CB repeating units in the resulting 2D polymer has been characterized using gold nanoparticle labeling and scanning transmission electron microscopy. Furthermore, we have confirmed the generality of our synthetic approach by applying it to different monomers to generate 2D polymers. Novel 2D polymers, such as our CB derived polymer, may be useful in selective transport, controlled drug delivery, and chemical sensing and may even serve as well-defined 2D scaffolds for ordered functionalization and platforms for bottom-up 3D construction.