We demonstrate a scalable architecture for a high-power, high-brightness, solid-state laser based on coherent combinations of master oscillator power amplifier chains. A common master oscillator injects a sequence of multikilowatt Nd:YAG zigzag slab amplifiers. Adaptive optics correct the wavefront of each amplified beamlet. The beamlets are tiled side by side and actively phase locked to form a single output beam. The laser produces 19 kW with beam quality <2x diffraction limited. To the best of our knowledge, this is the brightest cw solid-state laser demonstrated to date.