We describe an Astrometric Telescope Facility (ATF) which is intended to be operated on the Space Station in the 1990's. The main purpose of the telescope will be to do long-term, highly accurate relative astrometry of nearby stars to detect gravitational perturbations by companions with masses as small as Neptune. This will require astrometry accurate to 10 microarcseconds, at least 100 times better than that currently being done at ground-based observatories, and the operation of a facility in space for many years. Because the NASA Space Station is expected to be a permanent and continuously occupied base in low earth orbit, the system described here involves an articulated telescope mount at one of the upper points of attachment on the Space Station structure. The astrometric technique developed by Gatewood et al. (1980) will be used, in which the relative positions of star images in the focal plane of the telescope are indicated by the relative phases of the modulations of star brightnesses introduced by translating a Ronchi ruling across the focal plane at uniform speed. This technique has been proven to be capable of precise astrometry from Allegheny Observatory and when freed from the effects of the earth's atmosphere should provide the required accuracy. Technical issues under consideration include the damping of vibrations on the Space Station, required accuracy of fine guiding, optical configuration, metric accuracy of the Ronchi ruling, and choice of detectors.