We demonstrate a 10.7-eV (λ = 115.6 nm) laser with mW levels of average power and a 1-MHz repetition rate, which was driven by the third harmonic radiation (THG), at 347 nm, of an Yb:fiber chirped pulse amplifier (CPA) laser. The 347 nm ultraviolet radiation was obtained by frequency conversion of the high power output of a 1-MHz Yb:fiber CPA, using beta barium borate (BBO) nonlinear crystals. The frequency converted output was focused down into a gas cell filled with a mixture of Ar and Xe, and was subjected to a second THG frequency conversion. The generated 10.7-eV laser was separated from the fundamental beam using a LiF prism and no further separation from other harmonic waves was required. The highest measured output power was ~80 μW, which corresponded to an average power of ~1.25 mW inside the gas cell when the transmission coefficients of the LiF optics were taken into account. The corresponding conversion efficiency from 347 nm down to 115.6 nm was ~2.5 × 10-4.