To safely carry out its experimental program, the Laboratory for Laser Energetics (LLE) at the University of Rochester has commissioned the design, fabrication, and installation of a Tritium Removal System to clean up the various exhaust streams and to control tritium activity in the glove-boxes. This system, which is described in this paper, is optimized for minimum environmental impact and maximum personnel safety. It uses the best available technologies to extract tritium from inert gas streams in the elemental form. The various technologies considered and the rationale for their selection are discussed in detail. This approach reduces the volumes of effluent that require treatment to the extent practical and also avoids the need to oxidize HT to HTO with its higher radiotoxicity, thereby contributing to safety.