How does a cause lead to an effect, and which intermediate causal steps explain their connection? This work scrutinizes the mechanistic causal reasoning capabilities of large language models (LLMs) to answer these questions through the task of implicit causal chain discovery. In a diagnostic evaluation framework, we instruct nine LLMs to generate all possible intermediate causal steps linking given cause-effect pairs in causal chain structures. These pairs are drawn from recent resources in argumentation studies featuring polarized discussion on climate change. Our analysis reveals that LLMs vary in the number and granularity of causal steps they produce. Although they are generally self-consistent and confident about the intermediate causal connections in the generated chains, their judgments are mainly driven by associative pattern matching rather than genuine causal reasoning. Nonetheless, human evaluations confirmed the logical coherence and integrity of the generated chains. Our baseline causal chain discovery approach, insights from our diagnostic evaluation, and benchmark dataset with causal chains lay a solid foundation for advancing future work in implicit, mechanistic causal reasoning in argumentation settings.