A high precision star tracker was developed for the attitude measurement and control system of the German X-ray astronomy satellite ROSAT, which was launched on 1 June 1990. This star tracker has a basic pointing angle of around 0.5 arc second per axis in a 5.9 deg x 4.4 deg field of view, whilst tracking stars down to 7th magnitude. It also has to operate with reduced accuracy in the sky survey phase of the mission, when stars scan across the field of viewin a given direction with a rate of up to 5 /minute. The performance exceeds specification as demonstrated by ground test and flight data reported in this paper. The star tracker is a solid-state instrument based on a CCD image sensor. It has been qualified since 1985, and is the highest accuracy solid-state tracker flown by western European industrie to date.