THE astronomical soft X-ray background has both extragalactic and, at lower energies, galactic components. Using the Roentgen Astronomy Satellite (ROSAT), we have detected shadowing of the X-ray background in the ¼ keV band (presumed to be of galactic origin) by the unusual interstellar cloud in Draco. The Draco cloud is at high galactic latitude and, at several hundred parsecs distance from the Sun, is well away from the galactic plane. It reduces the ¼ keV emission by 63% relative to the adjacent sky, implying that a substantial contribution to the X-ray background in this direction comes from hot gas beyond the cloud. This is the first direct evidence for a million-degree galactic halo of gas, but the significance of this observation for understanding the global diffuse X-ray background is unclear, as it contradicts earlier studies1-3 which failed to find shadowing by galactic gas. More observations of this sort, covering objects distributed throughout the galaxy, are needed to explore the morphology of the hot and cold gas in the nearby interstellar medium.