Toxic interactions in Open Source Software (OSS) communities reduce contributor engagement and threaten project sustainability. Preventing such toxicity before it emerges requires a clear understanding of how harmful conversations unfold. However, most proactive moderation strategies are manual, requiring significant time and effort from community maintainers. To support more scalable approaches, we curate a dataset of 159 derailed toxic threads and 207 non-toxic threads from GitHub discussions. Our analysis reveals that toxicity can be forecast by tension triggers, sentiment shifts, and specific conversational patterns. We present a novel Large Language Model (LLM)-based framework for predicting conversational derailment on GitHub using a two-step prompting pipeline. First, we generate \textit{Summaries of Conversation Dynamics} (SCDs) via Least-to-Most (LtM) prompting; then we use these summaries to estimate the \textit{likelihood of derailment}. Evaluated on Qwen and Llama models, our LtM strategy achieves F1-scores of 0.901 and 0.852, respectively, at a decision threshold of 0.3, outperforming established NLP baselines on conversation derailment. External validation on a dataset of 308 GitHub issue threads (65 toxic, 243 non-toxic) yields an F1-score up to 0.797. Our findings demonstrate the effectiveness of structured LLM prompting for early detection of conversational derailment in OSS, enabling proactive and explainable moderation.