In this Letter we report new evidence for a close three-galaxy interaction in the compact group of galaxies HCG 95. Deep optical imaging in the Johnson UBVRI bands and in narrowband H alpha have shown four long tidal tails emanating from the two disk galaxies as well as signs of transfer of material between one of the tidal tails and the elliptical galaxy of the system. An unusual color gradient, likely related to an obscuring patch of dust, has been found in the elliptical galaxy. This fact, together with the morphology observed for the extended H alpha emission of the elliptical galaxy, gives further support to the thesis of the transfer of mass between the tidal tail and this galaxy. We argue that these three galaxies will probably merge in a few orbital periods; therefore, this system may represent a useful empirical test of what theoretical models have predicted for the evolution of compact groups.