The recent advances in Large Language Models (LLMs) have stimulated interest among researchers and industry professionals, particularly in their application to tasks concerning mobile user interfaces (UIs). This position paper investigates the use of LLMs for UI layout generation. Central to our exploration is the introduction of \textit{UI grammar} –– a novel approach we proposed to represent the hierarchical structure inherent in UI screens. The aim of this approach is to guide the generative capacities of LLMs more effectively and improve the explainability and controllability of the process. Initial experiments conducted with GPT-4 showed the promising capability of LLMs to produce high-quality user interfaces via in-context learning. Furthermore, our preliminary comparative study suggested the potential of the grammar-based approach in improving the quality of generative results in specific aspects.