The central region of the Coma cluster of galaxies was observed in the energy band from 0.065 to 0.245 kiloelectron volts by the Deep Survey telescope aboard the Extreme Ultraviolet Explorer. A diffuse emission halo of angular diameter ~30 arc minutes was detected. The extreme-ultraviolet (EUV) emission level exceeds that expected from the x-ray temperature gas in Coma. This hale suggests the presence of two more phases in the emitting gas, one at a temperature of ~2 x 106 kelvin and the other at ~8 x 105 kelvin. The letter phase cools rapidly and, in steady state, would have produced cold matter with a mass of ~1014 solar masses within the EUV halo. Although a similar EUV enhancement was discovered in the Virgo cluster, this detection in Coma applies to a noncooling flow system.