Large language models (LLMs) have shown significant potential for robotics applications, particularly task planning, by harnessing their language comprehension and text generation capabilities. However, in applications such as household robotics, a critical gap remains in the personalization of these models to household preferences. For example, an LLM planner may find it challenging to perform tasks that require personalization, such as deciding where to place mugs in a kitchen based on specific household preferences. We introduce LLM-Personalize, a novel framework designed to personalize LLM planners for household robotics. LLM-Personalize uses an LLM planner to perform iterative planning in multi-room, partially-observable household environments, utilizing a scene graph built dynamically from local observations. To personalize the LLM planner towards user preferences, our optimization pipeline integrates imitation learning and reinforced Self-Training. We evaluate LLM-Personalize on Housekeep, a challenging simulated real-world 3D benchmark for household rearrangements, demonstrating a more than 30 percent increase in success rate over existing LLM planners, showcasing significantly improved alignment with human preferences.