Cultural Intelligence (CQ) refers to the ability to understand unfamiliar cultural contexts-a crucial skill for large language models (LLMs) to effectively engage with globally diverse users. While existing research often focuses on explicitly stated cultural norms, such approaches fail to capture the subtle, implicit values that underlie real-world conversations. To address this gap, we introduce CQ-Bench, a benchmark specifically designed to assess LLMs' capability to infer implicit cultural values from natural conversational contexts. We generate a multi-character conversation-based stories dataset using values from the World Value Survey and GlobalOpinions datasets, with topics including ethical, religious, social, and political. Our dataset construction pipeline includes rigorous validation procedures-incorporation, consistency, and implicitness checks-using GPT-4o, with 98.2% human-model agreement in the final validation. Our benchmark consists of three tasks of increasing complexity: attitude detection, value selection, and value extraction. We find that while o1 and Deepseek-R1 models reach human-level performance in value selection (0.809 and 0.814), they still fall short in nuanced attitude detection, with F1 scores of 0.622 and 0.635, respectively. In the value extraction task, GPT-4o-mini and o3-mini score 0.602 and 0.598, highlighting the difficulty of open-ended cultural reasoning. Notably, fine-tuning smaller models (e.g., LLaMA-3.2-3B) on only 500 culturally rich examples improves performance by over 10%, even outperforming stronger baselines (o3-mini) in some cases. Using CQ-Bench, we provide insights into the current challenges in LLMs' CQ research and suggest practical pathways for enhancing LLMs' cross-cultural reasoning abilities.