Watermarking for large language models (LLMs) offers a promising approach to identifying AI-generated text. Existing approaches, however, either compromise the distribution of original generated text by LLMs or are limited to embedding zero-bit information that only allows for watermark detection but ignores identification. We present StealthInk, a stealthy multi-bit watermarking scheme that preserves the original text distribution while enabling the embedding of provenance data, such as userID, TimeStamp, and modelID, within LLM-generated text. This enhances fast traceability without requiring access to the language model's API or prompts. We derive a lower bound on the number of tokens necessary for watermark detection at a fixed equal error rate, which provides insights on how to enhance the capacity. Comprehensive empirical evaluations across diverse tasks highlight the stealthiness, detectability, and resilience of StealthInk, establishing it as an effective solution for LLM watermarking applications.