Context-aware Human Activity Recognition (HAR) is a hot research area in mobile computing, and the most effective solutions in the literature are based on supervised deep learning models. However, the actual deployment of these systems is limited by the scarcity of labeled data that is required for training. Neuro-Symbolic AI (NeSy) provides an interesting research direction to mitigate this issue, by infusing common-sense knowledge about human activities and the contexts in which they can be performed into HAR deep learning classifiers. Existing NeSy methods for context-aware HAR rely on knowledge encoded in logic-based models (e.g., ontologies) whose design, implementation, and maintenance to capture new activities and contexts require significant human engineering efforts, technical knowledge, and domain expertise. Recent works show that pre-trained Large Language Models (LLMs) effectively encode common-sense knowledge about human activities. In this work, we propose ContextGPT: a novel prompt engineering approach to retrieve from LLMs common-sense knowledge about the relationship between human activities and the context in which they are performed. Unlike ontologies, ContextGPT requires limited human effort and expertise. An extensive evaluation carried out on two public datasets shows how a NeSy model obtained by infusing common-sense knowledge from ContextGPT is effective in data scarcity scenarios, leading to similar (and sometimes better) recognition rates than logic-based approaches with a fraction of the effort.