While large language models (LLMs) are increasingly playing a pivotal role in education by providing instantaneous, adaptive responses, their potential to promote critical thinking remains understudied. In this paper, we fill such a gap and present an innovative educational chatbot designed to foster critical thinking through Socratic questioning. Unlike traditional intelligent tutoring systems, including educational chatbots, that tend to offer direct answers, the proposed Socratic tutor encourages students to explore various perspectives and engage in self-reflection by posing structured, thought-provoking questions. Our Socratic questioning is implemented by fine and prompt-tuning the open-source pretrained LLM with a specialized dataset that stimulates critical thinking and offers multiple viewpoints. In an effort to democratize access and to protect the students’ privacy, the proposed tutor is based on small LLMs (Llama2 7B and 13B-parameter models) that are able to run locally on off-the-shelf hardware. We validate our approach in a battery of experiments consisting of interactions between a simulated student and the chatbot to evaluate its effectiveness in enhancing critical thinking skills. Results indicate that the Socratic tutor supports the development of reflection and critical thinking significantly better than standard chatbots. Our approach opens the door for improving educational outcomes by cultivating active learning and encouraging intellectual autonomy.