Concerns regarding Large Language Models (LLMs) to memorize and disclose private information, particularly Personally Identifiable Information (PII), become prominent within the community. Many efforts have been made to mitigate the privacy risks.However, the mechanism through which LLMs memorize PII remains poorly understood. To bridge this gap, we introduce a pioneering method for pinpointing PII-sensitive neurons (privacy neurons) within LLMs. Our method employs learnable binary weight masks to localize specific neurons that account for the memorization of PII in LLMs through adversarial training. Our investigations discover that PII is memorized by a small subset of neurons across all layers, which shows the property of PII specificity. Furthermore, we propose to validate the potential in PII risk mitigation by deactivating the localized privacy neurons. Both quantitative and qualitative experiments demonstrate the effectiveness of our neuron localization algorithm.