A fuel injector has an actuator for generating a lifting movement and a lift translator filled with a hydraulic medium and deformable in the lifting direction, for transferring the lifting movement of the actuator to a valve needle, provision being made for a compensating chamber for the hydraulic medium, the compensating chamber being connected to an interior space of the lift translator via a throttle opening and enclosed by an elastic casing. Thus, temperature-related quasistatic deformations of actuator, lift translator, and/or valve needle can be compensated for by an exchange of the hydraulic medium between the interior space of the lift translator and the compensating chamber, while the comparatively fast lifting movements of the actuator are transmitted to the valve needle essentially without damping.