Conversational agents must translate egocentric utterances (e.g., "on my right") into allocentric orientations (N/E/S/W). This challenge is particularly critical in indoor or complex facilities where GPS signals are weak and detailed maps are unavailable. While chain-of-thought (CoT) prompting has advanced reasoning in language and vision tasks, its application to multimodal spatial orientation remains underexplored. We introduce Conversational Orientation Reasoning (COR), a new benchmark designed for Traditional Chinese conversational navigation projected from real-world environments, addressing egocentric-to-allocentric reasoning in non-English and ASR-transcribed scenarios. We propose a multimodal chain-of-thought (MCoT) framework, which integrates ASR-transcribed speech with landmark coordinates through a structured three-step reasoning process: (1) extracting spatial relations, (2) mapping coordinates to absolute directions, and (3) inferring user orientation. A curriculum learning strategy progressively builds these capabilities on Taiwan-LLM-13B-v2.0-Chat, a mid-sized model representative of resource-constrained settings. Experiments show that MCoT achieves 100% orientation accuracy on clean transcripts and 98.1% with ASR transcripts, substantially outperforming unimodal and non-structured baselines. Moreover, MCoT demonstrates robustness under noisy conversational conditions, including ASR recognition errors and multilingual code-switching. The model also maintains high accuracy in cross-domain evaluation and resilience to linguistic variation, domain shift, and referential ambiguity. These findings highlight the potential of structured MCoT spatial reasoning as a path toward interpretable and resource-efficient embodied navigation.