We demonstrate that graphene nanoribbons (GNRs) produced by the oxidative unzipping of carbon nanotubes can be chemically functionalized by diazonium salts. We show that functional groups form a thin layer on a GNR and modify its electrical properties. The kinetics of the functionalization can be monitored by probing the electrical properties of GNRs, either in vacuum after the grafting, or in situ in the solution. We derive a simple kinetics model that describes the change in the electrical properties of GNRs. The reaction of GNRs with 4-nitrobenzene diazonium tetrafluoroborate is reasonably fast, such that >60% of the maximum change in the electrical properties is observed after less than 5 min of grafting at room temperature.