The 2009 Global Trajectory Optimization Contest challenged participants to design a trajectory leaving from the Earth and traveling to rendezvous with one near-Earth asteroid in a time frame of ten years, while intercepting as many asteroids as possible along the way. The spacecraft was specified as having an initial mass of 1500 kg, and an ion engine capable of providing 0.135 N of thrust with a specific impulse of 3000 s. The objective function J was the number of intermediate targets intercepted. The dual objective of maximizing the final mass of the spacecraft was to be used only in the event of a tie. In the solution presented here, a heuristic spiral method was invented and used to generate a near-feasible sequence of asteroids to visit. Then a direct transcription method was used to find the corresponding trajectory maximizing the spacecraft mass while ensuring satisfaction of the equations of motion, the initial constraints at the Earth, the intercept constraints at each intermediate target, and the rendezvous constraints at the final target. A sequence of 21 asteroids was found, with a final spacecraft mass of 524 kg.