Finding all the words on a Boggle board is a classic computer programming problem. With a fast Boggle solver, local optimization techniques such as hillclimbing and simulated annealing can be used to find particularly high-scoring boards. The sheer number of possible Boggle boards has historically prevented an exhaustive search for the global optimum board. We apply Branch and Bound and a decision diagram-like data structure to perform the first such search. We find that the highest-scoring boards found via hillclimbing are, in fact, the global optima.