We report on nonlinear pulse compression at very high average power. A high-power fiber chirped pulse amplification system based on a novel large pitch photonic crystal fiber delivers $700\mathrm{fs}$ pulses with $200\mathrm{\mu J}$ pulse energy at a $1\mathrm{MHz}$ repetition rate, resulting in $200\mathrm{W}$ of average power. Subsequent spectral broadening in a xenon-filled hollow-core fiber and pulse compression with chirped mirrors is employed for pulse shortening and peak power enhancement. For the first time, to our knowledge, more than $100\mathrm{W}$ of average power are transmitted through a noble-gas-filled hollow fiber. After pulse compression of $81\mathrm{fs}$ , $93\mathrm{\mu J}$ pulses are obtained at a $1\mathrm{MHz}$ repetition rate.