The proliferation of hateful content in online videos poses severe threats to individual well-being and societal harmony. However, existing solutions for video hate detection either rely heavily on large-scale human annotations or lack fine-grained temporal precision. In this work, we propose LELA, the first training-free Large Language Model (LLM) based framework for hate video localization. Distinct from state-of-the-art models that depend on supervised pipelines, LELA leverages LLMs and modality-specific captioning to detect and temporally localize hateful content in a training-free manner. Our method decomposes a video into five modalities, including image, speech, OCR, music, and video context, and uses a multi-stage prompting scheme to compute fine-grained hateful scores for each frame. We further introduce a composition matching mechanism to enhance cross-modal reasoning. Experiments on two challenging benchmarks, HateMM and MultiHateClip, demonstrate that LELA outperforms all existing training-free baselines by a large margin. We also provide extensive ablations and qualitative visualizations, establishing LELA as a strong foundation for scalable and interpretable hate video localization.