We report the first experimental demonstration (to our knowledge) of high-order harmonic generation in rare gases driven by a state-of-the-art high-power Yb-doped-fiber chirped-pulse amplification system. The fiber laser delivers 270 fs pulses in the 30-100 microJ energy range at repetition rates varying from 100 kHz to 1 MHz. A proper focalization allows reaching several 10(13) W/cm2 in a gas jet. We have been able to produce and detect harmonics up to order 31 (33.2 nm) in Ar at a 100 kHz repetition rate. High-order harmonic generation at 1 MHz is also demonstrated in Xe up to harmonic 15. The demonstrated extreme UV (XUV) source will bring ultrashort XUV coincidence experiments from synchrotron facilities to tabletop laboratories.