The sensor-based recognition of Activities of Daily Living (ADLs) in smart home environments enables several applications in the areas of energy management, safety, well-being, and healthcare. ADL recognition is typically based on deep learning methods requiring large datasets to be trained. Recently, several studies proved that Large Language Models (LLMs) effectively capture common-sense knowledge about human activities. However, the effectiveness of LLMs for ADL recognition in smart home environments still deserves to be investigated. In this work, we propose ADL-LLM, a novel LLM-based ADL recognition system. ADL-LLM transforms raw sensor data into textual representations, that are processed by an LLM to perform zero-shot ADL recognition. Moreover, in the scenario where a small labeled dataset is available, ADL-LLM can also be empowered with few-shot prompting. We evaluated ADL-LLM on two public datasets, showing its effectiveness in this domain.