A fuel injector for injecting fuel into a combustion chamber of an internal combustion engine. A fuel supply line enters an injector housing from a high-pressure fuel source which can be hydraulically connected to a pressure chamber. A 3/2 directional control valve for injecting fuel into the combustion chamber has a valve piston which can be moved axially back and forth between a rest position and an injection position. The 3/2 directional control valve, by a first end face of the valve piston, is hydraulically coupled to and can be activated by a piezoelectric actuator. The 3/2 directional control has a ball element which is connected to a second end face of the valve piston and, in the rest position, can be moved against a first sealing edge and, in the injection position, can be moved against a second sealing edge.