Interpretability tools that offer explanations in the form of a dialogue have demonstrated their efficacy in enhancing users' understanding (Slack et al., 2023; Shen et al., 2023), as one-off explanations may fall short in providing sufficient information to the user. Current solutions for dialogue-based explanations, however, often require external tools and modules and are not easily transferable to tasks they were not designed for. With LLMCheckup, we present an easily accessible tool that allows users to chat with any state-of-the-art large language model (LLM) about its behavior. We enable LLMs to generate explanations and perform user intent recognition without fine-tuning, by connecting them with a broad spectrum of Explainable AI (XAI) methods, including white-box explainability tools such as feature attributions, and self-explanations (e.g., for rationale generation). LLM-based (self-)explanations are presented as an interactive dialogue that supports follow-up questions and generates suggestions. LLMCheckup provides tutorials for operations available in the system, catering to individuals with varying levels of expertise in XAI and supporting multiple input modalities. We introduce a new parsing strategy that substantially enhances the user intent recognition accuracy of the LLM. Finally, we showcase LLMCheckup for the tasks of fact checking and commonsense question answering.