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An ultrafast shutter has been developed for alteration of the time structure of synchrotron radiation from storage rings in the hard X-ray regime. In test applications on the wiggler beamline BW6 at DORIS, single bunches were extracted from the incident pulsed synchrotron radiation with minimum bunch-to-bunch distances of 482 ns. Even substantially shorter time windows may be defined in the case of tight collimation in the incident beam, e.g. on low-emittance sources. The shutter system is based on a new chopper concept involving a rotating X-ray mirror which totally reflects the incident radiation onto the sample through a remote slit. Rather low rotational velocities are sufficient to reach extremely short full open times. An additional shutter consisting of a slowly rotating disk prevents frame overlap and controls the repetition rate. A coincidence timing circuit checks the synchronization with the synchrotron bunch clock and provides trigger signals, e.g. for external excitation of a sample. The chopper system may be used, for example, in nanosecond time-resolved Laue diffraction experiments.