In the Traveling Salesman Problem (TSP), a list of cities and the distances between them are given. The goal is to find the shortest possible route that visits each city exactly once and returns to the original city. The TSP has a wide range of applications in many different industries including, but not limited to, optimizing mail and shipping routes, guiding industrial machines, mapping genomes, and improving autonomous vehicles. For centuries, traveling salesmen, politicians, and circuit preachers have tackled their own versions of the problem. Within the last century, the TSP has become one of the most important problems in the fields of mathematics and computer science. The time to find an exact solution is often impractically long, which has led to the development of numerous approximation techniques, ranging from linear programming methods to nature-inspired models. Here, we present a novel N-body approach to the TSP.