The brightness of nanometer‐sized field‐emission‐electron sources have been measured experimentally. Ultrasharp tungsten (111) single‐crystal tips were fabricatedinsituusing Ne sputtering and field evaporation, and monitored using field ion microscopy. The average brightness of single‐atom‐terminated nanotips was found to be 3.3×108A cm−2 sr−1at 470 V, or 7.7×1010A cm−2sr−1when extrapolated to 100 kV. These results show an improvement of about two orders of magnitude in source brightness over existing cold field‐emission‐electron sources, and produce a beam with greater particle flux per unit energy than those obtainable using current synchrotron/wiggler/undulator devices.