The amount of hazardous debris in Earth orbit has been increasing, posing an ever-greater danger to space assets and crewed missions. In January of 2007, a Chinese ASAT test produced approximately 2; 600 pieces of orbital debris. In February of 2009, Iridium 33 collided with an inactive Russian satellite, yielding approximately 1; 300 pieces of debris. These recent disastrous events and the sheer size of the Earth orbiting population make clear the necessity of removing orbital debris. In fact, experts from both NASA and ESA have stated that 10 to 20 pieces of orbital debris need to be removed per year to stabilize the orbital debris environment. However, no spacecraft trajectories have yet been designed for removing multiple debris objects and the size of the debris population makes the design of such trajectories a daunting task. Designing an efficient spacecraft trajectory to rendezvous with each of a large number of orbital debris pieces is akin to the famous Traveling Salesman problem, an NP-complete combinatorial optimization problem in which N cities are to be visited in turn. The goal is to choose the order in which the cities are visited so as to minimize the total path distance traveled. In the case of orbital debris, the pieces of debris to be visited must be selected and ordered such that spacecraft fuel consumption is minimized or at least kept low enough to be feasible. Emergent Space Technologies, Inc. has developed specialized algorithms for designing efficient tour missions for Near-Earth Asteroids that may be applied to the design of efficient spacecraft missions capable of visiting large numbers of orbital debris pieces. The first step is to identify a list of high priority debris targets using the Analytical Graphics, Inc. SOCRATES website and then obtain their state information from Celestrak. The tour trajectory design algorithms will then be used to determine the itinerary of objects and ΔV requirements. These results will shed light on how many debris pieces can be visited for various amounts of propellant, which launch vehicles can accommodate such missions, and how much margin is available for debris removal system payloads.