Electron transport through metal-molecule contacts greatly affects the operation and performance of electronic devices based on organic semiconductors(1-4) and is at the heart of molecular electronics exploiting single-molecule junctions(5-8). Much of our understanding of the charge injection and extraction processes in these systems relies on our knowledge of the potential barrier at the contact. Despite significant experimental and theoretical advances a clear rationale of the contact barrier at the single-molecule level is still missing. Here, we use scanning tunnelling microscopy to probe directly the nanocontact between a single molecule and a metal electrode in unprecedented detail. Our experiments show a significant variation on the submolecular scale. The local barrier modulation across an isolated 4-[trans-2-(pyrid-4-yl-vinyl)] benzoic acid molecule bound to a copper(111) electrode exceeds 1 eV. The giant modulation reflects the interaction between specific molecular groups and the metal and illustrates the critical processes determining the interface potential. Guided by our results, we introduce a new scheme to locally manipulate the potential barrier of the molecular nanocontacts with atomic precision.