We present the first demonstration of a thin-disk laser based on the gain material Yb:GGG. This material has many desirable properties for the thin-disk geometry: a high thermal conductivity, which is nearly independent of the doping concentration, a low quantum defect, low-temperature growth, and a broadband absorption spectrum, making it a promising contender to the well-established Yb:YAG for high-power applications. In continuous wave laser operation, we demonstrate output powers above 50 W, which is an order of magnitude higher than previously achieved with this material in the bulk geometry. We compare this performance with an Yb:YAG disk under identical pumping conditions and find comparable output characteristics (with typical optical-to-optical slope efficiencies >66%). Additionally, with the help of finite-element-method simulations, we show the advantageous heat-removal capabilities of Yb:GGG compared to Yb:YAG, resulting in >50% lower thermal lensing for thin Yb:GGG disks compared to Yb:YAG disks. The equivalent optical performance of the two crystals in combination with the easy growth and the significant thermal benefits of Yb:GGG show the large potential of future high-power thin-disk amplifiers and lasers based on this material, both for industrial and scientific applications.