The fabrication of 1 nm thin carbon nanoribbons and nanorings is demonstrated. Aromatic self-assembled monolayers are locally cross-linked by electron beam lithography into polymeric carbon nanosheets. Annealing at 1200 K in ultrahigh vacuum transforms these electrically insulating nanosheets into a conducting two-dimensional phase consisting of nanopatches of graphene with a sheet conductivity of similar to 10(-2) S sq. The method allows the direct writing of patterns into the monolayer, permitting the resistless fabrication of arbitrarily sized and shaped carbon nanostructures with a thickness of 1 nm.