This paper explores enhancing empathy in Large Language Models (LLMs) by integrating them with physiological data. We propose a physiological computing approach that includes developing deep learning models that use physiological data for recognizing psychological states and integrating the predicted states with LLMs for empathic interaction. We showcase the application of this approach in an Empathic LLM (EmLLM) chatbot for stress monitoring and control. We also discuss the results of a pilot study that evaluates this EmLLM chatbot based on its ability to accurately predict user stress, provide human-like responses, and assess the therapeutic alliance with the user.