Although large language models (LLMs) excel in complex reasoning tasks, they suffer from severe causal hallucination in event causality identification (ECI), particularly in smaller models ($\leq$1.5B parameters). A promising approach to address this issue is to fine-tune them with Chain-of-Thought (CoT) traces. However, there is currently a lack of CoT trace dataset available for ECI. In this paper, we first investigate the essential criteria that effective CoT traces should possess to mitigate causal hallucination in smaller models. We then design a pipeline to generate CoT traces that meet these criteria. Moreover, since there is currently no metric for quantifying causal hallucination, we also introduce a new metric, the Causal Hallucination Rate (CHR), to quantify causal hallucination, guide the formulation of effective CoT trace criteria, and validate the effectiveness of our pipeline. Our experiments show that fine-tuning with the CoT traces generated by our pipeline not only substantially reduces causal hallucination in smaller LLMs but also improves mean accuracy. Moreover, the fine-tuned models exhibit strong cross-dataset and cross-difficulty generalization, as well as robustness under misleading intervention prompts.