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 $270\mathrm{fs}$ pulses in the $30–100\mu \mathrm{J}$ energy range at repetition rates varying from $100\mathrm{kHz}$ to $1\mathrm{MHz}$ . A proper focalization allows reaching several ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$ in a gas jet. We have been able to produce and detect harmonics up to order 31 $\left(33.2\mathrm{nm}\right)$ in Ar at a $100\mathrm{kHz}$ repetition rate. High-order harmonic generation at $1\mathrm{MHz}$ 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.