Graphene nanostructures, where quantum confinement opens an energy gap in the band structure, hold promise for future electronic devices. To realize the full potential of these materials, atomic-scale control over the contacts to graphene and the graphene nanostructure forming the active part of the device is required. The contacts should have a high transmission and yet not modify the electronic properties of the active region significantly to maintain the potentially exciting physics offered by the nanoscale honeycomb lattice. Here we show how contacting an atomically well-defined graphene nanoribbon to a metallic lead by a chemical bond via only one atom significantly influences the charge transport through the graphene nanoribbon but does not affect its electronic structure. Specifically, we find that creating well-defined contacts can suppress inelastic transport channels.