Structural order emerging in the liquid state necessitates a critical degree of anisotropy of the molecules. For example, liquid crystals and Langmuir monolayers require rodor disc-shaped and long-chain amphiphilic molecules, respectively, to break the isotropic symmetry of liquids. In this Letter we present results from molecular dynamics simulations demonstrating that in two-dimensional liquids, a significantly smaller degree of anisotropy is sufficient to allow structural organization. In fact, the condensed phase of the smallest amphiphilic molecule, methanol, confined between two, or adsorbed on, graphene sheets forms a monolayer characterized by long chains of molecules. Intrachain interactions are dominated by hydrogen bonds, whereas interchain interactions are dispersive. Upon a decrease in density toward a gaslike state, these strings are transformed into rings. The two-dimensional liquid phase of methanol undergoes another transition upon cooling; in this case, the order−disorder transition is characterized by a low-temperature phase in which the hydrogen bond dipoles of neighboring strings adopt an antiparallel orientation.