The proliferation of Large Language Models (LLMs) has driven considerable interest in fine-tuning them with domain-specific data to create specialized language models. Nevertheless, such domain-specific fine-tuning data often contains contextually sensitive personally identifiable information (PII). Direct fine-tuning LLMs on this data without privacy protection poses a risk of data leakage of sensitive PII during inference time. To address this challenge, we introduce Contextual Privacy Protection Language Models (CPPLM), a novel paradigm for fine-tuning LLMs that effectively injects domain-specific knowledge while safeguarding inference-time data privacy. Our work offers a theoretical analysis for model design and delves into various techniques such as corpus curation, penalty-based unlikelihood in training loss, and instruction-based tuning, etc. Extensive experiments across diverse datasets and scenarios demonstrate the effectiveness of our approaches. In particular, instruction tuning with both positive and negative examples, stands out as a promising method, effectively protecting private data while enhancing the model s knowledge. Our work underscores the potential for Large Language Models as robust contextual privacy protection learners.