Picosecond x-ray pulses are extracted with a phase-locked x-ray pulse selector at 1.25 MHz repetition rate from the pulse trains of the accelerator-driven multiuser x-ray source BESSY II preserving the peak brilliance at high pulse purity. The system consists of a specially designed in-vacuum chopper wheel rotating with ≈ 1 kHz angular frequency. The wheel is driven in an ultrahigh vacuum and is levitated on magnetic bearings being capable of withstanding high centrifugal forces. Pulses are picked by 1252 high-precision slits of 70 μm width on the outer rim of the wheel corresponding to a temporal opening window of the chopper of 70 ns. We demonstrate how the electronic phase stabilization of ± 2 ns together with an arrival time jitter of the individual slits of the same order of magnitude allows us to pick short single bunch x-ray pulses out of a 200 ns ion clearing gap in a multibunch pulse train as emitted from a synchrotron facility at 1.25 MHz repetition rate with a pulse purity below the shot noise detection limit. The approach is applicable to any high-repetition pulsed radiation source, in particular in the x-ray spectral range up to 10 keV. The opening window in a real x-ray beamline, its stability, as well as the limits of mechanical pulse picking techniques in the MHz range are discussed.