We discuss the feasibility of a coherent optical telescope array, operated as a free-flying satellite, and capable of observing faint astronomical sources with very high angular resolution. In many ways, the coherent optical telescope array is directly analogous to the large radio astronomy arrays and very long baseline interferometers. A prototype instrument is discussed in detail, comprising four mirrors on a 10-meter baseline. This instrument could operate from the UV to the near-IR with one-dimensional resolution of 0.006 arc sec in the visible and achieve a faint object limit of about +25m in the visual. The field of view would be about 3 arc sec. In this article, we identify the principal technical problems associated with telescope arrays for astronomical observing and address certain of them. There is a long list of astronomical objects which could profitably be studied with milli-arc-sec resolution. Certainly one would include Seyfert nuclei, quasars, globular clusters, x-ray binaries, recent novae, binary stars, individual stars, asteroids, and planetary satellites. The ability to quickly produce an image, and to go to very faint objects, ensures that nearly all areas of astronomy will benefit from such an instrument.