A diode-pumped Yb:KLu(WO4)2 microchip laser passively Q-switched by a Cr4+:YAG saturable absorber generated a maximum average output power of 590 mW at 1031 nm with a slope efficiency of 55%. The pulse characteristics were 690 ps/47.6 μJ at a pulse repetition frequency of 12.4 kHz. The output beam had an excellent circular profile with M2<1.05. Yb:KLu(WO4)2 is very promising for ultrathin sub-ns microchip lasers.