Large language models (LLMs) have been widely applied for their remarkable capability of content generation. However, the practical use of open-source LLMs is hindered by high resource requirements, making deployment expensive and limiting widespread development. The collaborative inference is a promising solution for this problem, in which users collaborate by each hosting a subset of layers and transmitting intermediate activation. Many companies are building collaborative inference platforms to reduce LLM serving costs, leveraging users' underutilized GPUs. Despite widespread interest in collaborative inference within academia and industry, the privacy risks associated with LLM collaborative inference have not been well studied. This is largely because of the challenge posed by inverting LLM activation due to its strong non-linearity. In this paper, to validate the severity of privacy threats in LLM collaborative inference, we introduce the concept of prompt inversion attack (PIA), where a malicious participant intends to recover the input prompt through the activation transmitted by its previous participant. Specifically, we design a two-stage method to execute this attack. In the first stage, we optimize the input embedding with a constraint term derived from the LLM's embedding matrix to enforce the optimized embedding to be close to the ground truth. In the second stage, we accurately recover discrete tokens by incorporating activation calibration and semantic speculation. Extensive experiments show that our PIA method substantially outperforms existing baselines. For example, our method achieves an 88.4% token accuracy on the Skytrax dataset with the Llama-65B model when inverting the maximum number of transformer layers, while the best baseline method only achieves 22.8% accuracy. The results verify the effectiveness of our PIA attack and highlights its practical threat to LLM collaborative inference systems.