A simple, robust and compact pulse compressor for a high-repetition rate high-peak power fiber chirped pulse amplification system is presented. We use noble-gas-filled hollow fibers for spectral broadening of the optical pulses via self-phase modulation. Subsequent compression with chirped mirrors shortens the pulses by more than a factor of 10. Pulses shorter than 70 fs with pulse energies of the order of 100 mu J have been obtained resulting in a peak power up to 1 GW at 30.3kHz. Additionally, nonlinear polarization rotation has been used for temporal pulse cleaning during the nonlinear compression at 30.3 kHz and 100 kHz, respectively.