High-quality monoclinic KY(WO4)2 optical waveguides were grown by liquid-phase epitaxy, and laser operation of an Yb-doped KY(WO4)2 waveguide was demonstrated for the first time to our knowledge. Continuous-wave laser emission near 1 microm was achieved with both surface and buried planar waveguides. An output power of 290 mW was obtained in the fundamental mode and the slope efficiency was above 80%.