We demonstrate that nonlinear fiber compression is possible at unprecedented average power levels by use of a large-mode-area holey (microstructured) fiber and a passively mode-locked thin disk Yb:YAG laser operating at 1030 nm. We broaden the optical spectrum of the 810-fs pump pulses by nonlinear propagation in the fiber and remove the resultant chirp with a dispersive prism pair to achieve 18 W of average power in 33-fs pulses with a peak power of 12 MW and a repetition rate of 34 MHz. The output beam is nearly diffraction limited and is linearly polarized.