Computational methods for designing an optimal catalyst have recently received much attention, especially for energy-related applications. What is lacking in the previous methods is an explicit method to handle uncertainties in the complex models used, so that a robust design is achieved. This work proposes a stochastic optimization method for designing a robust catalyst. In particular, reactions involved in catalytic decomposition of ammonia are presented, and uncertainties associated with experimental determination of kinetic parameters are represented as exogenous variables with assumed probability distributions. The problem is formulated in terms of finding the optimal binding energies that maximize conversion in a microreactor. The resulting stochastic optimization problem is nonlinear, and involves the expectation operator as well as integration in the objective function. This difficult optimization problem is tackled by a population sample based approach, referred to as particle swarm optimization. The results show that the value of solving the stochastic problem is significant, and that it can provide a more robust solution compared to the certainty equivalence approach.