Personalization in large language models (LLMs) is increasingly important, aiming to align LLM's interactions, content, and recommendations with individual user preferences. Recent advances in LLM personalization have spotlighted effective prompt design, by enriching user queries with non-parametric knowledge through behavior history retrieval and textual profiles. However, these approaches were limited due to a lack of model ownership, resulting in constrained customization and privacy issues. Moreover, they often failed to accurately capture user behavior patterns, especially in cases where user data were complex and dynamic. To address these shortcomings, we introduce One PEFT Per User (OPPU), which employs personalized parameter-efficient fine-tuning (PEFT) modules, to store user-specific behavior patterns and preferences. By plugging in users' personal PEFT parameters, they can own and use their LLMs personally. OPPU integrates parametric user knowledge in the personal PEFT parameters with the non-parametric knowledge acquired through retrieval and profile. This integration adapts individual LLMs to user behavior shifts. Experimental results demonstrate that OPPU significantly outperforms existing prompt-based methods across seven diverse tasks in the LaMP benchmark. Further in-depth studies reveal OPPU's enhanced capabilities in handling user behavior shifts, modeling users at different active levels, maintaining robustness across various user history formats, and displaying versatility with different PEFT methods.