Imagine a world where you can access the power of large language models (LLMs) like ChatGPT without ever revealing your private data. This isn't science fiction, it's the promise of private inference using homomorphic encryption (HE). But until now, this powerful privacy-preserving technology has come at a steep cost: massive computational overhead and slow communication speeds. Enter FastQuery, a groundbreaking new framework that tackles these challenges head-on. Traditional HE-based methods for private LLM inference treat embedding table queries like any other matrix-vector multiplication. This approach ignores two crucial facts: user queries are one-hot vectors (meaning they select only one token from a vast vocabulary at a time), and embedding tables are surprisingly resilient to quantization noise (meaning we can use lower precision without sacrificing accuracy). FastQuery cleverly exploits these insights. It employs a communication-aware quantization algorithm to shrink the size of the encrypted data being transmitted. It also introduces a one-hot-aware dense packing algorithm that further streamlines the process. The result? A dramatic speed boost and a significant reduction in communication overhead. Compared to existing HE frameworks like Cheetah, Iron, and Bumblebee, FastQuery achieves several times faster performance with a fraction of the communication cost. This breakthrough opens doors to a new era of private AI applications. Imagine secure medical diagnoses using LLMs, personalized tutoring without revealing learning difficulties, or confidential business analysis without exposing sensitive company data. FastQuery brings these possibilities closer to reality. While FastQuery represents a major leap forward, challenges remain. Further research is needed to explore even more aggressive quantization strategies and optimize the framework for various hardware platforms. But one thing is clear: FastQuery has ignited a spark, illuminating the path towards a future where privacy and powerful AI go hand in hand.