In many areas of conceptual modeling, large language models (LLMs) can be applied as assistive technology, for example, to gather domain knowledge to support model creation or to generate models from text. However, there is limited work on using LLMs to support enterprise architecture (EA) modeling. An LLM-based approach for generating EA models from text must consistently incorporate the different architectural layers of an EA. The aim of this paper is to contribute to this area by analyzing existing research, designing an approach to generating LLM-based models from text, and evaluating it experimentally. More concretely, an LLM-based approach designed for enterprise models is adapted for EA modeling with ArchiMate. The results of the experiments not only confirm feasibility but also a decent level of model quality. A set of recommendations for practical LLM use in EA modeling is abstracted, and implications for future research are derived.