Conversational agents are getting increasingly popular and find applications in health and customer services. Conversations in these fields are often emotionally charged. It is, therefore, necessary to handle the conversation with some degree of empathy to be effective. In this work, we leverage advances in the field of natural language processing to create a dialogue system that can convincingly generate empathic responses to text-based messages. To improve the system's ability to converse with empathy, we train the language model on empathic conversations and inject additional emotional information in the response generation. We propose two chatbots: a benchmark bot and an empathic bot. Additionally, we implement an emotion classifier that allows us to predict the emotional state of text-based messages. We evaluate both chatbots in quantitative studies and compare them with human responses in qualitative studies involving human judges. Our evaluation shows that our empathic chatbot outperforms the benchmark bot and even the human-generated responses in terms of perceived empathy. Additionally, we achieve state-of-the-art results in terms of response quality using transformer-based language models. Finally we report that we can double the initial performance of the emotion classifier using undersampling techniques, yielding a final F1-score of 0.81 in six basic emotions.