The first demonstration of an Yb:YAl3(BO3)4 thin-disk laser is reported. An output power of 109 W with an optical efficiency of 50.2% was achieved in multimode CW-operation which is to the best of our knowledge a significant record performance compared to previous reports on CW-lasers with this material. At a lower power level of 19.3 W the material proved its suitability for efficient operation with an optical efficiency of 60.4%. In fundamental-mode operation the extracted output power was 10.4 W with an optical efficiency of 44.5% and a beam propagation factor M(2) = 1.39. The broad emission bandwidth of the material was confirmed by measuring a continuous wavelength tuning range from 1001 to 1053 nm with a maximum output power of 36 W at 1040 nm.