In high-mobility 6G scenarios, rapidly time-varying channels lead to very short coherence times, which makes conventional pilot-based channel state information (CSI) estimation approaches prone to outdated information or excessive pilot overhead. Therefore, channel prediction becomes essential in such dynamic wireless systems. To address this challenge, large language models (LLMs) are emerging learning frameworks that have recently attracted attention for CSI prediction due to their strong sequence modeling capability and ability to generalize across different environments. This paper proposes an LLM-based framework for channel prediction in high-mobility orthogonal time frequency space (OTFS) communication systems. In this work, we develop a physics-aware LLM-based predictor that learns the temporal evolution of OTFS channel coefficients from historical channel observations while incorporating mobility-related physical descriptors (e.g., maximum Doppler frequency) to achieve accurate prediction of future channel states in rapidly time-varying environments. The effectiveness of the proposed framework is evaluated through extensive simulations under user velocities ranging from 100 to 500 km/h. Numerical results show that the proposed method consistently achieves lower normalized mean square error (NMSE) compared with both classical deep learning predictors and LLM-based predictors without physical channel descriptors. These results demonstrate the advantage of integrating mobility-related channel knowledge with LLM-based sequence modeling for channel prediction in highly dynamic OTFS systems.