Large language models (LLMs) have achieved remarkable success across a wide range of tasks, particularly in natural language processing and computer vision. This success naturally raises an intriguing yet unexplored question: Can LLMs be harnessed to tackle channel state information (CSI) compression and feedback in massive multiple-input multiple-output (MIMO) systems? Efficient CSI feedback is a critical challenge in next-generation wireless communication. In this paper, we pioneer the use of LLMs for CSI compression, introducing a novel framework that leverages the powerful denoising capabilities of LLMs -- capable of error correction in language tasks -- to enhance CSI reconstruction performance. To effectively adapt LLMs to CSI data, we design customized pre-processing, embedding, and post-processing modules tailored to the unique characteristics of wireless signals. Extensive numerical results demonstrate the promising potential of LLMs in CSI feedback, opening up possibilities for this research direction.