We report identification of the first unambiguous example of what appears to be a new class of first-ascent giant stars that are actively accreting gas and dust and that are surrounded by substantial dusty disks. These old stars, who are nearing the end of their lives, are experiencing a rebirth into characteristics typically associated with newborn stars. The F2-type first-ascent giant star TYC 4144 329 2 is in a wide separation binary system with an otherwise normal G8 IV star, TYC 4144 329 1. From Keck near-infrared imaging and high-resolution spectroscopy we are able to determine that these two stars are $sim$1 Gyr old and reside at a distance of $sim$550 pc. One possible explanation for the origin of the accreting material is common-envelope interaction with a low-mass stellar or sub-stellar companion. The gaseous and dusty material around TYC 4144 329 2, as it is similar to the primordial disks observed around young classical T Tauri stars, could potentially give rise to a new generation of planets and/or planetesimals.