We demonstrate the first Kerr lens mode-locked Yb:CaGdAlO4 (Yb:CALGO) thin-disk laser oscillator. It generates pulses with a duration of 30 fs at a central wavelength of 1048 nm and a repetition rate of 124 MHz. The laser emits the shortest pulses generated by a thin-disk laser oscillator, equal to the shortest pulse duration obtained by Yb-doped bulk oscillators. The average output power is currently limited to 150 mW by the low gain and limited disk quality. We expect that more suitable Yb:CALGO disks will enable substantially higher power levels with similar pulse durations.