The invention relates to a fuel injector with an injector housing which has a high-pressure fuel connection which is connected to a central high-pressure fuel source outside the injector housing, and with a pressure chamber within the injector housing. According to the pressure in a coupling chamber, fuel under a high pressure is injected from the pressure chamber into a combustion chamber of an internal combustion engine when a nozzle valve opens. The nozzle valve has a combustion chamber-remote end with a control pressure surface which is acted upon in the coupling chamber by the coupling chamber pressure. In order to create a fuel injector which can be produced inexpensively, the nozzle valve has at least one low-pressure surface which is averted from the combustion chamber and acted upon with low pressure.