We report on the first laser operation of a novel double molybdate compound, Yb:KY(MoO4)2. Single-crystals were grown by the Low Temperature Gradient (LTG) Czochralski method. The crystal structure (orthorhombic, sp. gr. Pbna – D142h) was refined with the Rietveld method. Yb:KY(MoO4)2 exhibits a layered structure leading to a strong optical anisotropy and a perfect cleavage along the (100) plane. The stimulated-emission cross-section for Yb3+ ions is 3.70×10-20 cm2 at 1008.0 nm and the emission bandwidth is 37 nm (for light polarization E ||b). Continuous-wave laser operation is achieved in a 3 at.% Yb:KY(MoO4)2 crystal plate (thickness: 286 μm) under diode pumping. The microchip laser generated a maximum output power of 0.81 W at 1021-1044 nm with a slope efficiency of 76.4% and linear polarization. Yb:KY(MoO4)2 crystal films / plates are attractive for sub-ns passively Q-switched microchip lasers and thin-disk lasers.