Inferring demographic attributes such as age, sex, or income level from human mobility patterns enables critical applications such as targeted public health interventions, equitable urban planning, and personalized transportation services. Existing mobility-based demographic inference studies heavily rely on large-scale trajectory data with demographic labels, leading to limited interpretability and poor generalizability across different datasets and user groups. We propose HiCoTraj (Zero-Shot Demographic Reasoning via Hierarchical Chain-of-Thought Prompting from Trajectory), a framework that leverages LLMs' zero-shot learning and semantic understanding capabilities to perform demographic inference without labeled training data. HiCoTraj transforms trajectories into semantically rich, natural language representations by creating detailed activity chronicles and multi-scale visiting summaries. Then HiCoTraj uses a novel hierarchical chain of thought reasoning to systematically guide LLMs through three cognitive stages: factual feature extraction, behavioral pattern analysis, and demographic inference with structured output. This approach addresses the scarcity challenge of labeled demographic data while providing transparent reasoning chains. Experimental evaluation on real-world trajectory data demonstrates that HiCoTraj achieves competitive performance across multiple demographic attributes in zero-shot scenarios.