Nanoscale thermoelectricity is an attractive target technology, because it can convert ambient heat into electricity for powering embedded devices in the internet of things. We demonstrate that the thermoelectric performance of graphene nanoconstrictions can be significantly enhanced by the presence of stable radical adsorbates, because radical molecules adsorbed on the graphene nanoconstrictions create singly-occupied orbitals in the vicinity of Fermi energy. This in turn leads to sharp features in their transmission functions close to Fermi energy, which increases the electrical conductance and Seebeck coefficient of the nanoconstrictions. This is a generic feature of radical adsorbates and can be employed in the design of new thermoelectric devices and materials.