We report the serendipitous discovery of a bright point source flare in the Abell cluster A1795 with archival EUVE and Chandra observations. Assuming the EUVE emission is associated with the Chandra source, the X-ray 0.5-7 keV flux declined by a factor of ~2300 over a time span of 6 yr, following a power-law decay with index ~2.44 + or - 0.40. The Chandra data alone vary by a factor of ~20. The spectrum is well fit by a blackbody with a constant temperature of kT ~ 0.09 keV (~10 super(6) K). The flare is spatially coincident with the nuclear region of a faint, inactive galaxy with a photometric redshift consistent at the 1sigma level with the cluster (z = 0.062476). We argue that these properties are indicative of a tidal disruption of a star by a black hole (BH) with log(M sub(BH)/M sub(middot in circle)) ~ 5.5 + or - 0.5. If so, such a discovery indicates that tidal disruption flares may be used to probe BHs in the intermediate mass range, which are very difficult to study by other means.