Results of diode-pumped cw laser operation of an Yb3+:CaF2 single crystal are reported for what is to our knowledge the first time. With a 5-at.% Yb3+ -doped sample we obtained 5.8-W output power at 1053 nm for 15 W of incident power at 980 nm. The laser wavelength could be tuned from 1018 to 1072 nm, and a small-signal gain as high as 1.8 was achieved, showing the great potential of Yb3+:CaF2 as an amplifier medium for femtosecond pulses.