High power lasers operating at high repetition rates at the kilohertz regime are attractive for a variety of applications. Such high repetition rates can be achieved by Q-switching a cw laser using either an acousto-optic, an electro-optic or a passive Q-switch. Since passive Q-switching needs no external electric circuit, it may be valuable for solar pumped lasers to be used at space. In recent years, Cr4+:YAG has been extensively used for passive Q-switching of flashlamp pumped Nd:YAG lasers. For high average power lasers, the excellent thermal characteristics of Cr4+:YAG give it an edge over other saturable absorbers. In the present paper we report on the first passive Q-switching of solar pumped high power Nd:YAG laser. This solar pumped Nd:YAG laser, which employed 3 and 4 mm diameter Nd:YAG rods, emitted up to 50 watts in the cw mode. The laser rod was side-pumped by solar irradiation using a three-stage concentrating system. The Cr4+:YAG device rear surface was coated by high reflection dielectric coating, serving as cavity rear mirror, while the output mirror had a reflectivity of 90%. An average output power of 9 watts was obtained from the passive Q-switched solar pumped laser at 15 - 40 kHz, twice previous results for a passive Q- switched Nd:YAG laser, results which have been obtained under continuous flashlamp pumping.