Photometry and spectroscopy of the object Cha H[small alpha, Greek] 1, located in the Chamaeleon I star-forming cloud, show that it is a [tilde operator]106-year-old brown dwarf with spectral type M7.5 to M8 and 0.04 +/- 0.01 solar masses. Quiescent x-ray emission was detected in a 36-kilosecond observation with 31.4 +/- 7.7 x-ray photons, obtained with the Rontgen Satellite (ROSAT), with 9[small sigma, Greek] detection significance. This corresponds to an x-ray luminosity of 2.57 x 1028 ergs per second and an x-ray to bolometric luminosity ratio of 10-3.44. These are typical values for late M-type stars. Because the interior of brown dwarfs may be similar to that of convective late-type stars, which are well-known x-ray sources, x-ray emission from brown dwarfs may indicate magnetic activity.