Dialogue systems play an increasingly important role in various aspects of our daily life. It is evident from recent research that dialogue systems trained on human conversation data are biased. In particular, they can produce responses that reflect people's gender prejudice. Many debiasing methods have been developed for various NLP tasks, such as word embedding. However, they are not directly applicable to dialogue systems because they are likely to force dialogue models to generate similar responses for different genders. This greatly degrades the diversity of the generated responses and immensely hurts the performance of the dialogue models. In this paper, we propose a novel adversarial learning framework Debiased-Chat to train dialogue models free from gender bias while keeping their performance. Extensive experiments on two real-world conversation datasets show that our framework significantly reduces gender bias in dialogue models while maintaining the response quality. The implementation of the proposed framework is released.