Electron affinity, defined as the amount of energy necessary to remove an electron from an anion, plays a dominant role in reactivity. This is evidenced by halogen atoms whose electron affinities are larger than those of any other element in the periodic table. However, there exists a class of molecules whose electron affinities are even larger than those of halogen atoms. These molecules, referred to as superhalogens, typically consist of a central metal atom and several peripheral halogen or oxygen atoms. Using theoretical calculations based on density functional theory and experiments involving photoelectron spectroscopy we demonstrate that an entirely new class of electronegative species, which we term as “hyperhalogens”, can be created when halogen atoms are replaced by superhalogens as building blocks. These hyperhalogens can have electron affinities even larger than those of their superhalogen building blocks, thus opening the door to the synthesis of new materials.