Aeroassist guidance is concerned with providing steering commands to a vehicle flying through a planetary atmosphere in the form of an aerodynamic roll angle, or bank angle, which results in appropriate direction of the aerodynamic lift force so that the vehicle will safely and accurately reach its designated final condition. Aerocapture guidance is a particular subcategory of aeroassist guidance that involves atmospheric entry from an interplanetary transfer orbit, a guided flight through the atmosphere, and a final condition consisting of a post-atmospheric exit target orbit around the planet. Using aerocapture guidance to establish this target orbit can provide significant propellant mass savings when compared to traditional propulsive maneuvers. No current aerocapture guidance algorithms can ensure truly optimal performance in minimizing post-exit orbit insertion ΔV requirements. This thesis investigates the development of a two-phase optimal aerocapture guidance algorithm. This closed-loop guidance algorithm uses a mathematically optimal bang-bang bank angle profile structure, in which a vehicle first flies with the lift vector pointed straight up, and then flies full lift-down until atmospheric exit. The optimal trajectory is found by determining the switching time between full lift-up and full lift-down flight. Results from testing the algorithm in a high-fidelity NASA simulation environment are presented and compared with results from existing state-of-the-art aerocapture guidance algorithms. These results show that the developed algorithm provides the robustness and adaptability of a numerical predictor-corrector guidance algorithm while demonstrating a significant reduction in ΔV requirements compared to other existing algorithms.