Understanding human-scene contact remains a challenging task, as it requires detectors to simultaneously model the contacting body parts, their proximity to scene objects, and the overall scene context. In this work, we introduce GECO, a framework employing Large Language Models (LLMs) with the key insight that language offers a powerful prior to intuitively reason about 3D human-object and human-scene contact based on extensive multimodal world knowledge. By converting a body-vertex formulation to natural language descriptors, we enable zero-shot generation of vertex-level contact directly on the SMPL body. We show that GPT offers a surprisingly competitive baseline close to state-of-the-art detectors on the DAMON dataset. We apply and evaluate different emerging prompting paradigms, highlighting their potential and limitations towards LLM-based human-scene contact estimation.