Compact lasers capable of producing over kW peak power are highly desirable for applications including laser remote sensing, laser micromaching, and bio-medical photonics. We demonstrate a 50 kW peak power chip-scale vertical integrated optically coupled-cavity laser which consists of an electrically driven cavity with InGaAs quantum well for intra-cavity pumping of Yb:YAG and a passive Q-switch cavity with Yb:YAG/Cr:YAG. The laser produces pulses as short as 445 ps, the pulse energy of 26 µJ with the laser chip dimension of 1mm3. To the best of our knowledge, this is the first monolithic integration of semiconductor laser and solid-state laser producing over kW laser peak power.