Accurate short-term mobile traffic prediction is important for proactive resource allocation and low-latency network management in fifth generation (5G) and sixth generation (6G). While large language models (LLMs) can perform in-context learning (ICL) without task-specific retraining, naive ICL prompting may suffer from numerical instability and limited temporal reasoning when traffic dynamics fluctuate rapidly. In this paper, we propose a chain-of-thought (CoT)-enabled LLM-based mobile traffic prediction framework that operates in two phases: (i) an offline phase that constructs structured CoT demonstrations by generating rationales via a plan-based CoT (PCoT) pipeline (lecture, plan, and rationale), and (ii) an online phase that performs close to real-time prediction by retrieving the most relevant demonstrations using a similarity policy that considers both the historical throughput pattern and its short-term changes. We evaluate the proposed framework using a real-world 5G measurement dataset that includes both driving and static scenarios across diverse applications. Our numerical results reveal that the proposed 2-shot CoT-LLM can improve mean absolute error (MAE), root mean square error (RMSE) and R2-score by up to 14.88%, 15.03%, and 22.41%, respectively, compared to the 2-shot ICL-LLM and classical baselines. Furthermore, by optimizing the number of in-context examples, we achieve additional improvements of 4.58%, 5.70%, and 4.85% in MAE, RMSE, and R2-score, respectively.

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