The defining characteristic of a black hole is that it possesses an event horizon through which matter and energy can fall in but from which nothing escapes. Soft X-ray transients (SXTs), a class of X-ray binaries, appear to confirm this fundamental property of black holes. SXTs that are thought to contain accreting black holes display a large variation of luminosity between their bright and their faint states, while SXTs with accreting neutron stars have a smaller variation. This difference is predicted if the former stars have horizons, and the latter have normal surfaces. Subject headings: accretion, accretion disks — binaries: close — black hole physics — X-rays: stars 1