The optimization of nuclear engineering designs, such as nuclear fuel assembly configurations, involves managing competing objectives like reactivity control and power distribution. This study explores the use of Optimization by Prompting, an iterative approach utilizing large language models (LLMs), to address these challenges. The method is straightforward to implement, requiring no hyperparameter tuning or complex mathematical formulations. Optimization problems can be described in plain English, with only an evaluator and a parsing script needed for execution. The in-context learning capabilities of LLMs enable them to understand problem nuances, therefore, they have the potential to surpass traditional metaheuristic optimization methods. This study demonstrates the application of LLMs as optimizers to Boiling Water Reactor (BWR) fuel lattice design, showing the capability of commercial LLMs to achieve superior optimization results compared to traditional methods.