Only single-electron transistors with a certain level of cleanliness, where all states can be properly accessed, can be used for quantum experiments. To reveal their exceptional properties, carbon nanomaterials need to be stripped down to a single element: graphene has been exfoliated into a single sheet, and carbon nanotubes can reveal their vibrational, spin and quantum coherence properties only after being suspended across trenches^1–3. Molecular graphene nanoribbons^4–6 now provide carbon nanostructures with single-atom precision but suffer from poor solubility, similar to carbon nanotubes. Here we demonstrate the massive enhancement of the solubility of graphene nanoribbons by edge functionalization, to yield ultra-clean transport devices with sharp single-electron features. Strong electron–vibron coupling leads to a prominent Franck–Condon blockade, and the atomic definition of the edges allows identifying the associated transverse bending mode. These results demonstrate how molecular graphene can yield exceptionally clean electronic devices directly from solution. The sharpness of the electronic features opens a path to the exploitation of spin and vibrational properties in atomically precise graphene nanostructures.